Theorem dveeq2

Quantifier introduction when one pair of variables is distinct. Usage of this theorem is discouraged because it depends on [ax-13]. (Contributed by NM, 2-Jan-2002.) (Revised by NM, 20-Jul-2015.) Remove dependency on [ax-11]. (Revised by Wolf Lammen, 8-Sep-2018.) (New usage is discouraged.)

Conclusion
\( \vdash \neg \forall x \, x = y' \rightarrow z' = y' \rightarrow \forall x \, z' = y' \)
Proof
nfeqf2
nf5rd _