Theorem mpbi

Description: An inference from a biconditional, related to modus ponens. (Contributed by NM, 11-May-1993)

	Ref	Expression
Hypotheses	mpbi.min	⊢ 𝜑
	mpbi.maj	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	mpbi	⊢ 𝜓

Proof

Step	Hyp	Ref	Expression
1		mpbi.min	⊢ 𝜑
2		mpbi.maj	⊢ ( 𝜑 ↔ 𝜓 )
3	2	biimpi	⊢ ( 𝜑 → 𝜓 )
4	1 3	ax-mp	⊢ 𝜓