Theorem 2alim

Description: Theorem *11.32 in WhiteheadRussell p. 162. Theorem 19.20 of Margaris p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	2alim	$$⊢\forall x\forall y\left(\phi \to \psi \right)\to \left(\forall x\forall y\phi \to \forall x\forall y\psi \right)$$

Proof

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