Theorem alrimd

Description: Deduction form of Theorem 19.21 of Margaris p. 90, see 19.21 . (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	alrimd.1	$$⊢Ⅎx\phi$$
	alrimd.2	$$⊢Ⅎx\psi$$
	alrimd.3	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	alrimd	$$⊢\phi \to \left(\psi \to \forall x\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		alrimd.1	$$⊢Ⅎx\phi$$
2		alrimd.2	$$⊢Ⅎx\psi$$
3		alrimd.3	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	2	a1i	$$⊢\phi \to Ⅎx\psi$$
5	1 4 3	alrimdd	$$⊢\phi \to \left(\psi \to \forall x\chi \right)$$