Theorem bnj1517

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

	Ref	Expression
Hypothesis	bnj1517.1	$$⊢A=\left\{x|\left(\phi \wedge \psi \right)\right\}$$
Assertion	bnj1517	$$⊢x\in A\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1517.1	$$⊢A=\left\{x|\left(\phi \wedge \psi \right)\right\}$$
2	1	bnj1436	$$⊢x\in A\to \left(\phi \wedge \psi \right)$$
3	2	simprd	$$⊢x\in A\to \psi$$