Theorem mpbird

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 5-Aug-1993)

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

Proof

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