Theorem 2al2imi

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

	Ref	Expression
Hypothesis	2al2imi.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	2al2imi	$$⊢\forall x\forall y\phi \to \left(\forall x\forall y\psi \to \forall x\forall y\chi \right)$$

Proof

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