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Metamath Proof Explorer

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