Theorem iftruei

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

	Ref	Expression
Hypothesis	iftruei.1	$$⊢\phi$$
Assertion	iftruei	$$⊢if\left(\phi ,A,B\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		iftruei.1	$$⊢\phi$$
2		iftrue	$$⊢\phi \to if\left(\phi ,A,B\right)=A$$
3	1 2	ax-mp	$$⊢if\left(\phi ,A,B\right)=A$$