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Theorem pm2.21ddne 2366
Description: A contradiction implies anything. Equality/inequality deduction form. (Contributed by David Moews, 28-Feb-2017.)
Hypotheses
Ref Expression
pm2.21ddne.1  |-  ( ph  ->  A  =  B )
pm2.21ddne.2  |-  ( ph  ->  A  =/=  B )
Assertion
Ref Expression
pm2.21ddne  |-  ( ph  ->  ps )

Proof of Theorem pm2.21ddne
StepHypRef Expression
1 pm2.21ddne.1 . 2  |-  ( ph  ->  A  =  B )
2 pm2.21ddne.2 . . 3  |-  ( ph  ->  A  =/=  B )
32neneqd 2304 . 2  |-  ( ph  ->  -.  A  =  B )
41, 3pm2.21dd 592 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1314    =/= wne 2283
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in2 587
This theorem depends on definitions:  df-bi 116  df-ne 2284
This theorem is referenced by:  npnflt  9538  nmnfgt  9541  xlt2add  9603  xrbdtri  10985  divalglemex  11515  divalg  11517  znege1  11751  ennnfonelemex  11822
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