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Metamath Proof Explorer

Theorem iftruei

Description: Inference associated with iftrue . (Contributed by BJ, 7-Oct-2018)

Ref Expression
Hypothesis iftruei.1 ⊢ φ
Assertion iftruei ⊢ if φ A B = A

Proof

Step Hyp Ref Expression
1 iftruei.1 ⊢ φ
2 iftrue ⊢ φ → if φ A B = A
3 1 2 ax-mp ⊢ if φ A B = A