Theorem cdeqcv 2983

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 2974	1 ⊢ CondEq(𝑥 = 𝑦 → 𝑥 = 𝑦)

Syntax hints:  CondEqwcdeq 2972

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-cdeq 2973

This theorem is referenced by: (None)