Theorem pm13.181 2876

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

Step	Hyp	Ref	Expression
1		eqcom 2629	. 2 |- ( A = B <-> B = A )
2		pm13.18 2875	. 2 |- ( ( B = A /\ B =/= C ) -> A =/= C )
3	1, 2	sylanb 489	1 |- ( ( A = B /\ B =/= C ) -> A =/= C )

Syntax hints:   -> wi 4   /\ wa 384   = wceq 1483   =/= wne 2794

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-cleq 2615  df-ne 2795

This theorem is referenced by:  fzprval  12401  frgrwopreglem5a  27175  ax6e2ndeqALT  39167