Theorem alcom

Description: Theorem 19.5 of Margaris p. 89. Use its weak version alcomw when it allows to avoid dependence on ax-11 . (Contributed by NM, 30-Jun-1993)

	Ref	Expression
Assertion	alcom	$$⊢\forall x\forall y\phi \leftrightarrow \forall y\forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		ax-11	$$⊢\forall x\forall y\phi \to \forall y\forall x\phi$$
2		ax-11	$$⊢\forall y\forall x\phi \to \forall x\forall y\phi$$
3	1 2	impbii	$$⊢\forall x\forall y\phi \leftrightarrow \forall y\forall x\phi$$