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Theorem neeq1d 2223
Description: Deduction for inequality. (Contributed by NM, 25-Oct-1999.)
Hypothesis
Ref Expression
neeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
neeq1d  |-  ( ph  ->  ( A  =/=  C  <->  B  =/=  C ) )

Proof of Theorem neeq1d
StepHypRef Expression
1 neeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 neeq1 2218 . 2  |-  ( A  =  B  ->  ( A  =/=  C  <->  B  =/=  C ) )
31, 2syl 14 1  |-  ( ph  ->  ( A  =/=  C  <->  B  =/=  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98    = wceq 1243    =/= wne 2204
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206
This theorem is referenced by:  neeq12d  2225  eqnetrd  2229  prnzg  3492  ialgcvg  9887  ialgcvga  9890
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