Theorem bnj1350

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

	Ref	Expression
Hypothesis	bnj1350.1	$$⊢\chi \to \forall x\chi$$
Assertion	bnj1350	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \forall x\left(\phi \wedge \psi \wedge \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bnj1350.1	$$⊢\chi \to \forall x\chi$$
2		ax-5	$$⊢\phi \to \forall x\phi$$
3		ax-5	$$⊢\psi \to \forall x\psi$$
4	2 3 1	hb3an	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \forall x\left(\phi \wedge \psi \wedge \chi \right)$$