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Metamath Proof Explorer

Theorem bnj1138

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	bnj1138.1	$⊢ A = B \cup C$
	Assertion	bnj1138	$⊢ X \in A \leftrightarrow (X \in B \lor X \in C)$

Step	Hyp	Ref	Expression
1		bnj1138.1	$⊢ A = B \cup C$
2	1	eleq2i	$⊢ X \in A \leftrightarrow X \in (B \cup C)$
3		elun	$⊢ X \in (B \cup C) \leftrightarrow (X \in B \lor X \in C)$
4	2 3	bitri	$⊢ X \in A \leftrightarrow (X \in B \lor X \in C)$