Theorem alimdh

Description: Deduction form of Theorem 19.20 of Margaris p. 90, see alim . (Contributed by NM, 4-Jan-2002)

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

Proof

Step	Hyp	Ref	Expression
1		alimdh.1	$$⊢\phi \to \forall x\phi$$
2		alimdh.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	2	al2imi	$$⊢\forall x\phi \to \left(\forall x\psi \to \forall x\chi \right)$$
4	1 3	syl	$$⊢\phi \to \left(\forall x\psi \to \forall x\chi \right)$$