Theorem bnj534

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

	Ref	Expression
Hypothesis	bnj534.1	$$⊢\chi \to \left(\exists x\phi \wedge \psi \right)$$
Assertion	bnj534	$$⊢\chi \to \exists x\left(\phi \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bnj534.1	$$⊢\chi \to \left(\exists x\phi \wedge \psi \right)$$
2		19.41v	$$⊢\exists x\left(\phi \wedge \psi \right)\leftrightarrow \left(\exists x\phi \wedge \psi \right)$$
3	1 2	sylibr	$$⊢\chi \to \exists x\left(\phi \wedge \psi \right)$$