Theorem alimd

Description: Deduction form of Theorem 19.20 of Margaris p. 90, see alim . See alimdh , alimdv for variants requiring fewer axioms. (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	alimd.1	$$⊢Ⅎx\phi$$
	alimd.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	alimd	$$⊢\phi \to \left(\forall x\psi \to \forall x\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		alimd.1	$$⊢Ⅎx\phi$$
2		alimd.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	1	nf5ri	$$⊢\phi \to \forall x\phi$$
4	3 2	alimdh	$$⊢\phi \to \left(\forall x\psi \to \forall x\chi \right)$$