Theorem bnj1352

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

	Ref	Expression
Hypothesis	bnj1352.1	$$⊢\psi \to \forall x\psi$$
Assertion	bnj1352	$$⊢\left(\phi \wedge \psi \right)\to \forall x\left(\phi \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bnj1352.1	$$⊢\psi \to \forall x\psi$$
2		ax-5	$$⊢\phi \to \forall x\phi$$
3	2 1	hban	$$⊢\left(\phi \wedge \psi \right)\to \forall x\left(\phi \wedge \psi \right)$$