Theorem iffalsed

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

	Ref	Expression
Hypothesis	iffalsed.1	|- ( ph -> -. ch )
Assertion	iffalsed	|- ( ph -> if ( ch , A , B ) = B )

Proof

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