Theorem mpbii

Description: An inference from a nested biconditional, related to modus ponens. (Contributed by NM, 16-May-1993) (Proof shortened by Wolf Lammen, 25-Oct-2012)

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

Proof

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