Theorem mpbiri

Description: An inference from a nested biconditional, related to modus ponens. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 25-Oct-2012)

	Ref	Expression
Hypotheses	mpbiri.min	⊢ 𝜒
	mpbiri.maj	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	mpbiri	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		mpbiri.min	⊢ 𝜒
2		mpbiri.maj	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
3	1	a1i	⊢ ( 𝜑 → 𝜒 )
4	3 2	mpbird	⊢ ( 𝜑 → 𝜓 )