Metamath Proof Explorer


Theorem cdeqth

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

Ref Expression
Hypothesis cdeqth.1
|- ph
Assertion cdeqth
|- CondEq ( x = y -> ph )

Proof

Step Hyp Ref Expression
1 cdeqth.1
 |-  ph
2 1 a1i
 |-  ( x = y -> ph )
3 2 cdeqi
 |-  CondEq ( x = y -> ph )