Theorem alrimdd

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

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

Proof

Step	Hyp	Ref	Expression
1		alrimdd.1	$$⊢Ⅎx\phi$$
2		alrimdd.2	$$⊢\phi \to Ⅎx\psi$$
3		alrimdd.3	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	2	nf5rd	$$⊢\phi \to \left(\psi \to \forall x\psi \right)$$
5	1 3	alimd	$$⊢\phi \to \left(\forall x\psi \to \forall x\chi \right)$$
6	4 5	syld	$$⊢\phi \to \left(\psi \to \forall x\chi \right)$$