Theorem alanimi

Description: Variant of al2imi with conjunctive antecedent. (Contributed by Andrew Salmon, 8-Jun-2011)

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

Proof

Step	Hyp	Ref	Expression
1		alanimi.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
2	1	ex	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	2	al2imi	$$⊢\forall x\phi \to \left(\forall x\psi \to \forall x\chi \right)$$
4	3	imp	$$⊢\left(\forall x\phi \wedge \forall x\psi \right)\to \forall x\chi$$