Theorem cdeqi

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

	Ref	Expression
Hypothesis	cdeqi.1	$$⊢x=y\to \phi$$
Assertion	cdeqi	$$⊢CondEq\left(x=y\to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		cdeqi.1	$$⊢x=y\to \phi$$
2		df-cdeq	$$⊢CondEq\left(x=y\to \phi \right)\leftrightarrow \left(x=y\to \phi \right)$$
3	1 2	mpbir	$$⊢CondEq\left(x=y\to \phi \right)$$