Theorem ax8v

Weakened version of [ax-8], with a disjoint variable condition on x , y. This should be the only proof referencing [ax-8], and it should be referenced only by its two weakened versions ax8v1 and ax8v2, from which [ax-8] is then rederived as ax8, which shows that either ax8v or the conjunction of ax8v1 and ax8v2 is sufficient. (Contributed by BJ, 7-Dec-2020.) Use ax8 instead. (New usage is discouraged.)

Conclusion
\( \vdash x' = y' \rightarrow x' \in z' \rightarrow y' \in z' \)
Proof
ax-8