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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 
|- A =/= B
nemtbir.2 
|- ( ph <-> A = B )
Assertion nemtbir 
|- -. ph

Proof

Step Hyp Ref Expression
1 nemtbir.1 
 |-  A =/= B
2 nemtbir.2 
 |-  ( ph <-> A = B )
3 1 neii 
 |-  -. A = B
4 3 2 mtbir 
 |-  -. ph