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	$$⊢\phi \to \neg \chi$$
Assertion	iffalsed	$$⊢\phi \to if\left(\chi ,A,B\right)=B$$

Proof

Step	Hyp	Ref	Expression
1		iffalsed.1	$$⊢\phi \to \neg \chi$$
2		iffalse	$$⊢\neg \chi \to if\left(\chi ,A,B\right)=B$$
3	1 2	syl	$$⊢\phi \to if\left(\chi ,A,B\right)=B$$