Theorem mpbid

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 21-Jun-1993)

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

Proof

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