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Theorem pm13.181 2715
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 2411 . 2  |-  ( A  =  B  <->  B  =  A )
2 pm13.18 2714 . 2  |-  ( ( B  =  A  /\  B  =/=  C )  ->  A  =/=  C )
31, 2sylanb 470 1  |-  ( ( A  =  B  /\  B  =/=  C )  ->  A  =/=  C )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367    = wceq 1405    =/= wne 2598
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-an 369  df-cleq 2394  df-ne 2600
This theorem is referenced by:  fzprval  11793  wwlkn0s  25109  ax6e2ndeqALT  36742
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