Theorem bj-axc14nf

Description: Proof of a version of axc14 using the "nonfree" idiom. (Contributed by BJ, 20-Oct-2021) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-axc14nf	$$⊢\neg \forall zz=x\to \left(\neg \forall zz=y\to Ⅎzx\in y\right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-nfeel2	$$⊢\neg \forall zz=x\to Ⅎzx\in t$$
2		elequ2	$$⊢t=y\to \left(x\in t\leftrightarrow x\in y\right)$$
3	1 2	bj-dvelimdv1	$$⊢\neg \forall zz=x\to \left(\neg \forall zz=y\to Ⅎzx\in y\right)$$