Theorem axc5c7

Description: Proof of a single axiom that can replace ax-c5 and ax-c7 . See axc5c7toc5 and axc5c7toc7 for the rederivation of those axioms. (Contributed by Scott Fenton, 12-Sep-2005) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	axc5c7	$$⊢\left(\forall x\neg \forall x\phi \to \forall x\phi \right)\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		ax-c7	$$⊢\neg \forall x\neg \forall x\phi \to \phi$$
2		ax-c5	$$⊢\forall x\phi \to \phi$$
3	1 2	ja	$$⊢\left(\forall x\neg \forall x\phi \to \forall x\phi \right)\to \phi$$