Theorem al2imi

Description: Inference quantifying antecedent, nested antecedent, and consequent. (Contributed by NM, 10-Jan-1993)

	Ref	Expression
Hypothesis	al2imi.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	al2imi	$$⊢\forall x\phi \to \left(\forall x\psi \to \forall x\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		al2imi.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		al2im	$$⊢\forall x\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\forall x\phi \to \left(\forall x\psi \to \forall x\chi \right)\right)$$
3	2 1	mpg	$$⊢\forall x\phi \to \left(\forall x\psi \to \forall x\chi \right)$$