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Theorem syl5eqner 2626
Description: B chained equality inference for inequality. (Contributed by NM, 6-Jun-2012.)
Hypotheses
Ref Expression
syl5eqner.1  |-  B  =  A
syl5eqner.2  |-  ( ph  ->  B  =/=  C )
Assertion
Ref Expression
syl5eqner  |-  ( ph  ->  A  =/=  C )

Proof of Theorem syl5eqner
StepHypRef Expression
1 syl5eqner.2 . 2  |-  ( ph  ->  B  =/=  C )
2 syl5eqner.1 . . 3  |-  B  =  A
32neeq1i 2611 . 2  |-  ( B  =/=  C  <->  A  =/=  C )
41, 3sylib 189 1  |-  ( ph  ->  A  =/=  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652    =/= wne 2599
This theorem is referenced by:  fclsfnflim  18059  ptcmplem2  18084  vieta1lem1  20227  vieta1lem2  20228  cdleme3h  31032  cdleme7ga  31045
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-cleq 2429  df-ne 2601
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