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Metamath Proof Explorer

Theorem bnj1212

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

	Ref	Expression
Hypotheses	bnj1212.1	$⊢ B = \{x \in A \| φ\}$
	bnj1212.2	$⊢ θ \leftrightarrow (χ \land x \in B \land τ)$
Assertion	bnj1212	$⊢ θ \to x \in A$

Step	Hyp	Ref	Expression
1		bnj1212.1	$⊢ B = \{x \in A \| φ\}$
2		bnj1212.2	$⊢ θ \leftrightarrow (χ \land x \in B \land τ)$
3	1	ssrab3	$⊢ B \subseteq A$
4	2	simp2bi	$⊢ θ \to x \in B$
5	3 4	bnj1213	$⊢ θ \to x \in A$