Theorem axc711to11

Description: Rederivation of ax-11 from axc711 . Note that ax-c7 and ax-11 are not used by the rederivation. (Contributed by NM, 18-Nov-2006) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	axc711to11	$$⊢\forall x\forall y\phi \to \forall y\forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		axc711toc7	$$⊢\neg \forall y\neg \forall y\neg \forall x\forall y\phi \to \neg \forall x\forall y\phi$$
2	1	con4i	$$⊢\forall x\forall y\phi \to \forall y\neg \forall y\neg \forall x\forall y\phi$$
3		axc711	$$⊢\neg \forall y\neg \forall x\forall y\phi \to \forall x\phi$$
4	3	alimi	$$⊢\forall y\neg \forall y\neg \forall x\forall y\phi \to \forall y\forall x\phi$$
5	2 4	syl	$$⊢\forall x\forall y\phi \to \forall y\forall x\phi$$