Theorem pm13.181 2287

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 2042	. 2 |- ( A = B <-> B = A )
2		pm13.18 2286	. 2 |- ( ( B = A /\ B =/= C ) -> A =/= C )
3	1, 2	sylanb 268	1 |- ( ( A = B /\ B =/= C ) -> A =/= C )

Syntax hints:   -> wi 4   /\ wa 97   = wceq 1243   =/= wne 2204

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206

This theorem is referenced by:  fzprval  8944