Theorem bnj1238

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

	Ref	Expression
Hypothesis	bnj1238.1	$$⊢\phi \leftrightarrow \exists x\in A\left(\psi \wedge \chi \right)$$
Assertion	bnj1238	$$⊢\phi \to \exists x\in A\psi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1238.1	$$⊢\phi \leftrightarrow \exists x\in A\left(\psi \wedge \chi \right)$$
2		bnj1239	$$⊢\exists x\in A\left(\psi \wedge \chi \right)\to \exists x\in A\psi$$
3	1 2	sylbi	$$⊢\phi \to \exists x\in A\psi$$