Theorem iffalsei

Description: Inference associated with iffalse . (Contributed by BJ, 7-Oct-2018)

	Ref	Expression
Hypothesis	iffalsei.1	$$⊢\neg \phi$$
Assertion	iffalsei	$$⊢if\left(\phi ,A,B\right)=B$$

Proof

Step	Hyp	Ref	Expression
1		iffalsei.1	$$⊢\neg \phi$$
2		iffalse	$$⊢\neg \phi \to if\left(\phi ,A,B\right)=B$$
3	1 2	ax-mp	$$⊢if\left(\phi ,A,B\right)=B$$