Theorem 2alanimi

Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Hypothesis	2alanimi.1	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
Assertion	2alanimi	$$⊢\left(\forall x\forall y\phi \wedge \forall x\forall y\psi \right)\to \forall x\forall y\chi$$

Proof

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