Theorem axc5c711toc5

Description: Rederivation of ax-c5 from axc5c711 . Only propositional calculus is used by the rederivation. (Contributed by NM, 19-Nov-2006) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	axc5c711toc5	$$⊢\forall x\phi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		ax-1	$$⊢\forall x\phi \to \left(\forall x\forall x\neg \forall x\forall x\phi \to \forall x\phi \right)$$
2		axc5c711	$$⊢\left(\forall x\forall x\neg \forall x\forall x\phi \to \forall x\phi \right)\to \phi$$
3	1 2	syl	$$⊢\forall x\phi \to \phi$$