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Theorem pm13.181 2519
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 2285 . 2  |-  ( A  =  B  <->  B  =  A )
2 pm13.18 2518 . 2  |-  ( ( B  =  A  /\  B  =/=  C )  ->  A  =/=  C )
31, 2sylanb 458 1  |-  ( ( A  =  B  /\  B  =/=  C )  ->  A  =/=  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    = wceq 1623    =/= wne 2446
This theorem is referenced by:  fzprval  10844  hdrmp  25706  a9e2ndeqALT  28708
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-cleq 2276  df-ne 2448
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