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Theorem nemtbir 2780
Description: An inference from an inequality, related to modus tollens. (Contributed by NM, 13-Apr-2007.)
Hypotheses
Ref Expression
nemtbir.1  |-  A  =/= 
B
nemtbir.2  |-  ( ph  <->  A  =  B )
Assertion
Ref Expression
nemtbir  |-  -.  ph

Proof of Theorem nemtbir
StepHypRef Expression
1 nemtbir.1 . . 3  |-  A  =/= 
B
21neii 2652 . 2  |-  -.  A  =  B
3 nemtbir.2 . 2  |-  ( ph  <->  A  =  B )
42, 3mtbir 299 1  |-  -.  ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    = wceq 1370    =/= wne 2648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-ne 2650
This theorem is referenced by:  opthwiener  4704  opthprc  4997  snnen2o  7613  cfpwsdom  8863  pmtrsn  16148  gzrngunitlem  18012  ex-id  23820  sltval2  27964  sltsolem1  27976
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