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Theorem neeq12d 2269
Description: Deduction for inequality. (Contributed by NM, 24-Jul-2012.)
Hypotheses
Ref Expression
neeq1d.1  |-  ( ph  ->  A  =  B )
neeq12d.2  |-  ( ph  ->  C  =  D )
Assertion
Ref Expression
neeq12d  |-  ( ph  ->  ( A  =/=  C  <->  B  =/=  D ) )

Proof of Theorem neeq12d
StepHypRef Expression
1 neeq1d.1 . . 3  |-  ( ph  ->  A  =  B )
21neeq1d 2267 . 2  |-  ( ph  ->  ( A  =/=  C  <->  B  =/=  C ) )
3 neeq12d.2 . . 3  |-  ( ph  ->  C  =  D )
43neeq2d 2268 . 2  |-  ( ph  ->  ( B  =/=  C  <->  B  =/=  D ) )
52, 4bitrd 186 1  |-  ( ph  ->  ( A  =/=  C  <->  B  =/=  D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> 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  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ne 2250
This theorem is referenced by:  3netr3d  2281  3netr4d  2282
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