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Theorem necon4bdOLD 2680
Description: Obsolete proof of necon4bd 2679 as of 23-Nov-2019. (Contributed by NM, 1-Jun-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
necon4bd.1  |-  ( ph  ->  ( -.  ps  ->  A  =/=  B ) )
Assertion
Ref Expression
necon4bdOLD  |-  ( ph  ->  ( A  =  B  ->  ps ) )

Proof of Theorem necon4bdOLD
StepHypRef Expression
1 nne 2658 . 2  |-  ( -.  A  =/=  B  <->  A  =  B )
2 necon4bd.1 . . 3  |-  ( ph  ->  ( -.  ps  ->  A  =/=  B ) )
32con1d 124 . 2  |-  ( ph  ->  ( -.  A  =/= 
B  ->  ps )
)
41, 3syl5bir 218 1  |-  ( ph  ->  ( A  =  B  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1395    =/= wne 2652
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 2654
This theorem is referenced by: (None)
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