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Metamath Proof Explorer

Theorem iftrued

Description: Value of the conditional operator when its first argument is true. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Hypothesis iftrued.1 ⊢ φ → χ
Assertion iftrued ⊢ φ → if χ A B = A

Proof

Step Hyp Ref Expression
1 iftrued.1 ⊢ φ → χ
2 iftrue ⊢ χ → if χ A B = A
3 1 2 syl ⊢ φ → if χ A B = A