Theorem ax6dgen

Description: Tarski's system uses the weaker ax6v instead of the bundled ax-6 , so here we show that the degenerate case of ax-6 can be derived. Even though ax-6 is in the list of axioms used, recall that in set.mm, the only statement referencing ax-6 is ax6v . We later rederive from ax6v the bundled form as ax6 with the help of the auxiliary axiom schemes. (Contributed by NM, 23-Apr-2017)

	Ref	Expression
Assertion	ax6dgen	$$⊢\neg \forall x\neg x=x$$

Proof

Step	Hyp	Ref	Expression
1		equid	$$⊢x=x$$
2	1	notnoti	$$⊢\neg \neg x=x$$
3	2	spfalw	$$⊢\forall x\neg x=x\to \neg x=x$$
4	1 3	mt2	$$⊢\neg \forall x\neg x=x$$