Theorem sylg

Description: A syllogism combined with generalization. Inference associated with sylgt . General form of alrimih . (Contributed by NM, 9-Jan-1993) Extract from proof of alrimih . (Revised by BJ, 4-Oct-2019)

	Ref	Expression
Hypotheses	sylg.1	$$⊢\phi \to \forall x\psi$$
	sylg.2	$$⊢\psi \to \chi$$
Assertion	sylg	$$⊢\phi \to \forall x\chi$$

Proof

Step	Hyp	Ref	Expression
1		sylg.1	$$⊢\phi \to \forall x\psi$$
2		sylg.2	$$⊢\psi \to \chi$$
3	2	alimi	$$⊢\forall x\psi \to \forall x\chi$$
4	1 3	syl	$$⊢\phi \to \forall x\chi$$