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Metamath Proof Explorer

Theorem uneqri

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

		Ref	Expression
	Hypothesis	uneqri.1	$⊢ (x \in A \lor x \in B) \leftrightarrow x \in C$
	Assertion	uneqri	$⊢ A \cup B = C$

Step	Hyp	Ref	Expression
1		uneqri.1	$⊢ (x \in A \lor x \in B) \leftrightarrow x \in C$
2		elun	$⊢ x \in (A \cup B) \leftrightarrow (x \in A \lor x \in B)$
3	2 1	bitri	$⊢ x \in (A \cup B) \leftrightarrow x \in C$
4	3	eqriv	$⊢ A \cup B = C$