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Theorem necon3bbii 2286
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 130 . . 3  |-  ( A  =  B  <->  ph )
32necon3abii 2285 . 2  |-  ( A  =/=  B  <->  -.  ph )
43bicomi 130 1  |-  ( -. 
ph 
<->  A  =/=  B )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103    = wceq 1285    =/= wne 2249
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115  df-ne 2250
This theorem is referenced by: (None)
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