Theorem bnj1538

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

	Ref	Expression
Hypothesis	bnj1538.1	$$⊢A=\left\{x\in B|\phi \right\}$$
Assertion	bnj1538	$$⊢x\in A\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1538.1	$$⊢A=\left\{x\in B|\phi \right\}$$
2	1	rabeq2i	$$⊢x\in A\leftrightarrow \left(x\in B\wedge \phi \right)$$
3	2	simprbi	$$⊢x\in A\to \phi$$