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 )