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Metamath Proof Explorer

Theorem eleq1i

Description: Inference from equality to equivalence of membership. (Contributed by NM, 21-Jun-1993)

		Ref	Expression
	Hypothesis	eleq1i.1	$⊢ A = B$
	Assertion	eleq1i	$⊢ A \in C \leftrightarrow B \in C$

Step	Hyp	Ref	Expression
1		eleq1i.1	$⊢ A = B$
2		eleq1	$⊢ A = B \to (A \in C \leftrightarrow B \in C)$
3	1 2	ax-mp	$⊢ A \in C \leftrightarrow B \in C$