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Theorem necon1adOLD 2660
Description: Obsolete proof of necon1ad 2659 as of 23-Nov-2019. (Contributed by NM, 2-Apr-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
necon1ad.1  |-  ( ph  ->  ( -.  ps  ->  A  =  B ) )
Assertion
Ref Expression
necon1adOLD  |-  ( ph  ->  ( A  =/=  B  ->  ps ) )

Proof of Theorem necon1adOLD
StepHypRef Expression
1 df-ne 2640 . 2  |-  ( A  =/=  B  <->  -.  A  =  B )
2 necon1ad.1 . . 3  |-  ( ph  ->  ( -.  ps  ->  A  =  B ) )
32con1d 124 . 2  |-  ( ph  ->  ( -.  A  =  B  ->  ps )
)
41, 3syl5bi 217 1  |-  ( ph  ->  ( A  =/=  B  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1383    =/= wne 2638
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 2640
This theorem is referenced by: (None)
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