Theorem ax6ev

Description: At least one individual exists. Weaker version of ax6e . When possible, use of this theorem rather than ax6e is preferred since its derivation is much shorter and requires fewer axioms. (Contributed by NM, 3-Aug-2017)

	Ref	Expression
Assertion	ax6ev	$$⊢\exists xx=y$$

Proof

Step	Hyp	Ref	Expression
1		ax6v	$$⊢\neg \forall x\neg x=y$$
2		df-ex	$$⊢\exists xx=y\leftrightarrow \neg \forall x\neg x=y$$
3	1 2	mpbir	$$⊢\exists xx=y$$