Theorem alrimdv

Description: Deduction form of Theorem 19.21 of Margaris p. 90. See 19.21 and 19.21v . (Contributed by NM, 10-Feb-1997)

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

Proof

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