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Theorem necon4aiOLD 2635
Description: Obsolete proof of necon4ai 2634 as of 22-Nov-2019. (Contributed by NM, 16-Jan-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
necon4ai.1  |-  ( A  =/=  B  ->  -.  ph )
Assertion
Ref Expression
necon4aiOLD  |-  ( ph  ->  A  =  B )

Proof of Theorem necon4aiOLD
StepHypRef Expression
1 necon4ai.1 . . 3  |-  ( A  =/=  B  ->  -.  ph )
21con2i 120 . 2  |-  ( ph  ->  -.  A  =/=  B
)
3 nne 2597 . 2  |-  ( -.  A  =/=  B  <->  A  =  B )
42, 3sylib 196 1  |-  ( ph  ->  A  =  B )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1399    =/= wne 2591
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 2593
This theorem is referenced by: (None)
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