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Metamath Proof Explorer

Theorem mtbird

Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 10-May-1994)

Ref Expression
Hypotheses mtbird.min ⊢ φ → ¬ χ
mtbird.maj ⊢ φ → ψ ↔ χ
Assertion mtbird ⊢ φ → ¬ ψ

Proof

Step Hyp Ref Expression
1 mtbird.min ⊢ φ → ¬ χ
2 mtbird.maj ⊢ φ → ψ ↔ χ
3 2 biimpd ⊢ φ → ψ → χ
4 1 3 mtod ⊢ φ → ¬ ψ