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 φψχ
Assertion mtbird φ¬ψ

Proof

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