Metamath Proof Explorer

Theorem pm13.18OLD

Description: Obsolete version of pm13.18 as of 14-May-2023. (Contributed by Andrew Salmon, 3-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		eqeq1	$⊢ A = B \to (A = C \leftrightarrow B = C)$
2	1	biimprd	$⊢ A = B \to (B = C \to A = C)$
3	2	necon3d	$⊢ A = B \to (A \neq C \to B \neq C)$
4	3	imp	$⊢ (A = B \land A \neq C) \to B \neq C$