Theorem cdeqcv 3737

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 23	. 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦)
2	1	cdeqi 3728	1 ⊢ CondEq(𝑥 = 𝑦 → 𝑥 = 𝑦)

This proof depends on syntax axioms:  CondEqwcdeq 3726

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-cdeq 3727

This theorem is used by: (None)