Theorem bnj1265

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

	Ref	Expression
Hypothesis	bnj1265.1	$$⊢\phi \to \exists x\in A\psi$$
Assertion	bnj1265	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1265.1	$$⊢\phi \to \exists x\in A\psi$$
2	1	bnj1196	$$⊢\phi \to \exists x\left(x\in A\wedge \psi \right)$$
3	2	bnj1266	$$⊢\phi \to \exists x\psi$$
4	3	bnj937	$$⊢\phi \to \psi$$