Theorem axc5c7toc7

Description: Rederivation of ax-c7 from axc5c7 . Only propositional calculus is used for the rederivation. (Contributed by Scott Fenton, 12-Sep-2005) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	axc5c7toc7	$$⊢\neg \forall x\neg \forall x\phi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$$⊢\neg \forall x\neg \forall x\phi \to \left(\forall x\neg \forall x\phi \to \forall x\phi \right)$$
2		axc5c7	$$⊢\left(\forall x\neg \forall x\phi \to \forall x\phi \right)\to \phi$$
3	1 2	syl	$$⊢\neg \forall x\neg \forall x\phi \to \phi$$