Theorem pm13.181

Description: Theorem *13.181 in WhiteheadRussell p. 178. (Contributed by Andrew Salmon, 3-Jun-2011) (Proof shortened by Wolf Lammen, 30-Oct-2024)

	Ref	Expression
Assertion	pm13.181	|- ( ( A = B /\ B =/= C ) -> A =/= C )

Proof

Step	Hyp	Ref	Expression
1		neeq1	|- ( A = B -> ( A =/= C <-> B =/= C ) )
2	1	biimpar	|- ( ( A = B /\ B =/= C ) -> A =/= C )