Theorem mpbidi

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994)

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

Proof

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