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	$$⊢\phi \to \chi$$
Assertion	iftrued	$$⊢\phi \to if\left(\chi ,A,B\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		iftrued.1	$$⊢\phi \to \chi$$
2		iftrue	$$⊢\chi \to if\left(\chi ,A,B\right)=A$$
3	1 2	syl	$$⊢\phi \to if\left(\chi ,A,B\right)=A$$