Theorem 2alimdv

Description: Deduction form of Theorem 19.20 of Margaris p. 90 with two quantifiers, see alim . (Contributed by NM, 27-Apr-2004)

	Ref	Expression
Hypothesis	2alimdv.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	2alimdv	$$⊢\phi \to \left(\forall x\forall y\psi \to \forall x\forall y\chi \right)$$

Proof

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