Theorem iftrued

Description: Value of the conditional operator when its first argument is true. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypothesis	iftrued.1	⊢ ( 𝜑 → 𝜒 )
Assertion	iftrued	⊢ ( 𝜑 → if ( 𝜒 , 𝐴 , 𝐵 ) = 𝐴 )

Proof

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