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


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