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I have Elsha of the Infinite on the battlefield, who has prowess:

Whenever you cast a noncreature spell, this creature gets +1/+1 until end of turn.

Her prowess triggered five times, making her a 8/8 until end of turn. She moves to combat.

An opponent then flashes in Ixidron:

As Ixidron enters the battlefield, turn all other nontoken creatures face down. (They're 2/2 creatures.)

Looking at the rulings of 4/27/2018:

Creatures turned face down by Ixidron are 2/2 creatures with no text, no name, no subtypes, no expansion symbol, and no mana cost. These values are copiable if an object becomes a copy of one of those creatures, and their normal values are not copiable.

Does this mean that the temporary amount of +1/+1 from prowess remain until end of turn, even though Elsha got flipped? Or does the "with no text" remove it altogether? So is my attacking creature a 7/7 until end of turn, or just a 2/2?

Yes, the creature's power and toughness are increased for the rest of the turn even after it is turned face down.

The +1/+1 buffs from Prowess are continuous effects that affect the creature until end of turn. A creature that is turned face down is still the same creature, so continuous effects that affected it before continue to affect it.

The Prowess ability is defined in rule 702.107a:

Prowess is a triggered ability. “Prowess” means “Whenever you cast a noncreature spell, this creature gets +1/+1 until end of turn.”

The effect "this creature gets +1/+1 until end of turn" is a continuous effect. The following rules in the Continuous Effects rules section apply:

• 
  611.1. A continuous effect modifies characteristics of objects, modifies control of objects, or affects players or the rules of the game, for a fixed or indefinite period.


• 
  611.2. A continuous effect may be generated by the resolution of a spell or ability.
  
  
  • 
    611.2a A continuous effect generated by the resolution of a spell or ability lasts as long as stated by the spell or ability creating it (such as “until end of turn”). If no duration is stated, it lasts until the end of the game.
  
  

The "+1/+1" modification affects power and toughness, which are characteristics as defined in rule 109.3:

An object’s characteristics are name, mana cost, color, color indicator, card type, subtype, supertype, rules text, abilities, power, toughness, loyalty, hand modifier, and life modifier. Objects can have some or all of these characteristics. Any other information about an object isn’t a characteristic. For example, characteristics don’t include whether a permanent is tapped, a spell’s target, an object’s owner or controller, what an Aura enchants, and so on.

Rule 7007.2a describes turning permanents face down:

If a face-up permanent is turned face down by a spell or ability that doesn’t list any characteristics for that object, it becomes a 2/2 face-down creature with no text, no name, no subtypes, and no mana cost. A permanent that enters the battlefield face down also has these characteristics unless otherwise specified by the effect that put it onto the battlefield face down or allowed it to be cast face down. These values are the copiable values of that object’s characteristics.

In addition, the following rules about status apply:

• 
  110.5. A permanent’s status is its physical state. There are four status categories, each of which has two possible values: tapped/untapped, flipped/unflipped, face up/face down, and phased in/phased out. Each permanent always has one of these values for each of these categories.
  
  
  • 
    110.5a Status is not a characteristic, though it may affect a permanent’s characteristics.
  
  

As with other status changes like tapped/untapped, changing a creature from face up to face down does not make it a different object, so effects like the one from Prowess continue to apply to it.