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Theorem necon3bbii 2364
Description: Deduction from equality to inequality. (Contributed by NM, 13-Apr-2007.)
Hypothesis
Ref Expression
necon3bbii.1  |-  ( ph  <->  A  =  B )
Assertion
Ref Expression
necon3bbii  |-  ( -. 
ph 
<->  A  =/=  B )

Proof of Theorem necon3bbii
StepHypRef Expression
1 necon3bbii.1 . . . 4  |-  ( ph  <->  A  =  B )
21bicomi 131 . . 3  |-  ( A  =  B  <->  ph )
32necon3abii 2363 . 2  |-  ( A  =/=  B  <->  -.  ph )
43bicomi 131 1  |-  ( -. 
ph 
<->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104    = wceq 1335    =/= wne 2327
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 604  ax-in2 605
This theorem depends on definitions:  df-bi 116  df-ne 2328
This theorem is referenced by:  ef0lem  11557
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