Theorem iffalsei

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

	Ref	Expression
Hypothesis	iffalsei.1	⊢ ¬ 𝜑
Assertion	iffalsei	⊢ if ( 𝜑 , 𝐴 , 𝐵 ) = 𝐵

Proof

Step	Hyp	Ref	Expression
1		iffalsei.1	⊢ ¬ 𝜑
2		iffalse	⊢ ( ¬ 𝜑 → if ( 𝜑 , 𝐴 , 𝐵 ) = 𝐵 )
3	1 2	ax-mp	⊢ if ( 𝜑 , 𝐴 , 𝐵 ) = 𝐵