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Metamath Proof Explorer

Theorem pm13.18

Description: Theorem *13.18 in WhiteheadRussell p. 178. (Contributed by Andrew Salmon, 3-Jun-2011) (Proof shortened by Wolf Lammen, 29-Oct-2024)

		Ref	Expression
	Assertion	pm13.18	$⊢ (A = B \land A \neq C) \to B \neq C$

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