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Metamath Proof Explorer

Theorem eqeltr

Description: Substitution of equal classes into element relation. (Contributed by Peter Mazsa, 22-Jul-2017)

		Ref	Expression
	Assertion	eqeltr	$⊢ (A = B \land B \in C) \to A \in C$

Step	Hyp	Ref	Expression
1		eleq1	$⊢ A = B \to (A \in C \leftrightarrow B \in C)$
2	1	biimpar	$⊢ (A = B \land B \in C) \to A \in C$