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, 14-May-2023)

		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	biimpd	$⊢ A = B \to (A \neq C \to B \neq C)$
3	2	imp	$⊢ (A = B \land A \neq C) \to B \neq C$