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Theorem neeq2d 2301
Description: Deduction for inequality. (Contributed by NM, 25-Oct-1999.)
Hypothesis
Ref Expression
neeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
neeq2d  |-  ( ph  ->  ( C  =/=  A  <->  C  =/=  B ) )

Proof of Theorem neeq2d
StepHypRef Expression
1 neeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 neeq2 2296 . 2  |-  ( A  =  B  ->  ( C  =/=  A  <->  C  =/=  B ) )
31, 2syl 14 1  |-  ( ph  ->  ( C  =/=  A  <->  C  =/=  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    = wceq 1314    =/= wne 2282
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-4 1470  ax-17 1489  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2283
This theorem is referenced by:  neeq12d  2302  neeqtrd  2310  sqrt2irr  11686  ennnfonelemk  11758  ennnfoneleminc  11769  ennnfonelemex  11772  ennnfonelemnn0  11780  ennnfonelemr  11781
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