bv-idvar

Theorem.

Arguments:

z (sv), x (sv), y (sv),

Assertions:

(z bound in forallx(xeqy))

Proof:

Hyp Ref Line Expr
ax121(lnotforallz(zeqx)to(lnotforallz(zeqy)to((xeqy)toforallz(xeqy))))
ax42(forallx(xeqy)to(xeqy))
1, 2rpi433(lnotforallz(zeqx)to(lnotforallz(zeqy)to(forallx(xeqy)toforallz(xeqy))))
ax104(forallx(xeqz)to(forallx(xeqy)toforallz(xeqy)))
4aleqcom5(forallz(zeqx)to(forallx(xeqy)toforallz(xeqy)))
ax106(forally(yeqz)to(forally(xeqy)toforallz(xeqy)))
ax107(forallx(xeqy)to(forallx(xeqy)toforally(xeqy)))
7imabs8(forallx(xeqy)toforally(xeqy))
6, 8rpi329(forally(yeqz)to(forallx(xeqy)toforallz(xeqy)))
9aleqcom10(forallz(zeqy)to(forallx(xeqy)toforallz(xeqy)))
3, 5, 10caseii11(forallx(xeqy)toforallz(xeqy))
11ax512(forallx(xeqy)toforallxforallz(xeqy))
ax713(forallxforallz(xeqy)toforallzforallx(xeqy))
12, 13syl14(forallx(xeqy)toforallzforallx(xeqy))
14df-Bvp15(z bound in forallx(xeqy))