Theorem 19.29

Description: Theorem 19.29 of Margaris p. 90. See also 19.29r . (Contributed by NM, 21-Jun-1993) (Proof shortened by Andrew Salmon, 13-May-2011)

	Ref	Expression
Assertion	19.29	$$⊢\left(\forall x\phi \wedge \exists x\psi \right)\to \exists x\left(\phi \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm3.2	$$⊢\phi \to \left(\psi \to \left(\phi \wedge \psi \right)\right)$$
2	1	aleximi	$$⊢\forall x\phi \to \left(\exists x\psi \to \exists x\left(\phi \wedge \psi \right)\right)$$
3	2	imp	$$⊢\left(\forall x\phi \wedge \exists x\psi \right)\to \exists x\left(\phi \wedge \psi \right)$$