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	⊢ ( 𝜑 → ¬ 𝜒 )
Assertion	iffalsed	⊢ ( 𝜑 → if ( 𝜒 , 𝐴 , 𝐵 ) = 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		iffalsed.1	⊢ ( 𝜑 → ¬ 𝜒 )
2		iffalse	⊢ ( ¬ 𝜒 → if ( 𝜒 , 𝐴 , 𝐵 ) = 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → if ( 𝜒 , 𝐴 , 𝐵 ) = 𝐵 )