Theorem alimdv

Description: Deduction form of Theorem 19.20 of Margaris p. 90, see alim . See alimdh and alimd for versions without a distinct variable condition. (Contributed by NM, 3-Apr-1994)

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

Proof

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