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Theorem pm13.181 2492
Description: Theorem *13.181 in [WhiteheadRussell] p. 178. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.181  |-  ( ( A  =  B  /\  B  =/=  C )  ->  A  =/=  C )

Proof of Theorem pm13.181
StepHypRef Expression
1 eqcom 2258 . 2  |-  ( A  =  B  <->  B  =  A )
2 pm13.18 2491 . 2  |-  ( ( B  =  A  /\  B  =/=  C )  ->  A  =/=  C )
31, 2sylanb 460 1  |-  ( ( A  =  B  /\  B  =/=  C )  ->  A  =/=  C )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360    = wceq 1619    =/= wne 2419
This theorem is referenced by:  fzprval  10796  hdrmp  25059  a9e2ndeqALT  27742
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-17 1628  ax-4 1692  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-an 362  df-nf 1540  df-cleq 2249  df-ne 2421
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