Metamath Proof Explorer


Theorem cdeqth

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

Ref Expression
Hypothesis cdeqth.1 φ
Assertion cdeqth CondEq x = y φ

Proof

Step Hyp Ref Expression
1 cdeqth.1 φ
2 1 a1i x = y φ
3 2 cdeqi CondEq x = y φ