Theorem iftruei

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

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

Proof

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