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Theorem pm2.21ddne 2768
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 2656 . 2  |-  ( ph  ->  -.  A  =  B )
41, 3pm2.21dd 174 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1398    =/= wne 2649
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 2651
This theorem is referenced by:  cshwshashlem2  14668  dprdsn  17281  coseq00topi  23064  tglndim0  24213  ncolncol  24230  footne  24301  sgnsub  28750  sgnmulsgn  28755  sgnmulsgp  28756  pconcon  28943  fnchoice  31647  osumcllem11N  36106  dochexmidlem8  37610
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