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Theorem pm2.21ddne 2303
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 2241 . 2  |-  ( ph  ->  -.  A  =  B )
41, 3pm2.21dd 560 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1259    =/= wne 2220
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-ne 2221
This theorem is referenced by:  divalglemex  10234  divalg  10236
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