This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ (A = B \land B \neq C) \to A \neq C$

Step	Hyp	Ref	Expression
1		neeq1	$⊢ A = B \to (A \neq C \leftrightarrow B \neq C)$
2	1	biimpar	$⊢ (A = B \land B \neq C) \to A \neq C$