Theorem cdeqth 2811

Description: Deduce conditional equality from a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
cdeqth.1	⊢ 𝜑

Assertion

Ref	Expression
cdeqth	⊢ CondEq(𝑥 = 𝑦 → 𝜑)

Proof of Theorem cdeqth

Step	Hyp	Ref	Expression
1		cdeqth.1	. . 3 ⊢ 𝜑
2	1	a1i 9	. 2 ⊢ (𝑥 = 𝑦 → 𝜑)
3	2	cdeqi 2809	1 ⊢ CondEq(𝑥 = 𝑦 → 𝜑)

Syntax hints:  CondEqwcdeq 2807

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 2808

This theorem is referenced by:  cdeqal1  2815  cdeqab1  2816  nfccdeq  2822