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	|- ( ph -> ch )
Assertion	iftrued	|- ( ph -> if ( ch , A , B ) = A )

Proof

Step	Hyp	Ref	Expression
1		iftrued.1	|- ( ph -> ch )
2		iftrue	|- ( ch -> if ( ch , A , B ) = A )
3	1 2	syl	|- ( ph -> if ( ch , A , B ) = A )