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Theorem necon3bbid 2325
Description: Deduction from equality to inequality. (Contributed by NM, 2-Jun-2007.)
Hypothesis
Ref Expression
necon3bbid.1  |-  ( ph  ->  ( ps  <->  A  =  B ) )
Assertion
Ref Expression
necon3bbid  |-  ( ph  ->  ( -.  ps  <->  A  =/=  B ) )

Proof of Theorem necon3bbid
StepHypRef Expression
1 necon3bbid.1 . . . 4  |-  ( ph  ->  ( ps  <->  A  =  B ) )
21bicomd 140 . . 3  |-  ( ph  ->  ( A  =  B  <->  ps ) )
32necon3abid 2324 . 2  |-  ( ph  ->  ( A  =/=  B  <->  -. 
ps ) )
43bicomd 140 1  |-  ( ph  ->  ( -.  ps  <->  A  =/=  B ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 104    = wceq 1316    =/= wne 2285
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589
This theorem depends on definitions:  df-bi 116  df-ne 2286
This theorem is referenced by:  necon3bid  2326  eldifsn  3620  prmrp  11750
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