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Metamath Proof Explorer

Theorem eqeq2i

Description: Inference from equality to equivalence of equalities. (Contributed by NM, 26-May-1993)

		Ref	Expression
	Hypothesis	eqeq2i.1	$⊢ A = B$
	Assertion	eqeq2i	$⊢ C = A \leftrightarrow C = B$

Step	Hyp	Ref	Expression
1		eqeq2i.1	$⊢ A = B$
2		eqeq2	$⊢ A = B \to (C = A \leftrightarrow C = B)$
3	1 2	ax-mp	$⊢ C = A \leftrightarrow C = B$