Theorem bnj1266

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

	Ref	Expression
Hypothesis	bnj1266.1	$$⊢\chi \to \exists x\left(\phi \wedge \psi \right)$$
Assertion	bnj1266	$$⊢\chi \to \exists x\psi$$

Proof

Step	Hyp	Ref	Expression
1		bnj1266.1	$$⊢\chi \to \exists x\left(\phi \wedge \psi \right)$$
2		simpr	$$⊢\left(\phi \wedge \psi \right)\to \psi$$
3	1 2	bnj593	$$⊢\chi \to \exists x\psi$$