Theorem cdeqi

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

	Ref	Expression
Hypothesis	cdeqi.1	⊢ ( 𝑥 = 𝑦 → 𝜑 )
Assertion	cdeqi	⊢ CondEq ( 𝑥 = 𝑦 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		cdeqi.1	⊢ ( 𝑥 = 𝑦 → 𝜑 )
2		df-cdeq	⊢ ( CondEq ( 𝑥 = 𝑦 → 𝜑 ) ↔ ( 𝑥 = 𝑦 → 𝜑 ) )
3	1 2	mpbir	⊢ CondEq ( 𝑥 = 𝑦 → 𝜑 )