Theorem cdeqcv 2809

Description: Conditional equality for set-to-class promotion. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
cdeqcv	⊢ CondEq(𝑥 = 𝑦 → 𝑥 = 𝑦)

Proof of Theorem cdeqcv

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦)
2	1	cdeqi 2800	1 ⊢ CondEq(𝑥 = 𝑦 → 𝑥 = 𝑦)

Syntax hints:  CondEqwcdeq 2798

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-cdeq 2799

This theorem is referenced by: (None)