Metamath Proof Explorer


Theorem nemtbir

Description: An inference from an inequality, related to modus tollens. (Contributed by NM, 13-Apr-2007)

Ref Expression
Hypotheses nemtbir.1 AB
nemtbir.2 φA=B
Assertion nemtbir ¬φ

Proof

Step Hyp Ref Expression
1 nemtbir.1 AB
2 nemtbir.2 φA=B
3 1 neii ¬A=B
4 3 2 mtbir ¬φ