dveeq1

Theorem.

Arguments:

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

Dummy variables:

w (sv),

Distinct variable conditions:

(w, x), (w, y), (w, z), (x, z),

Assertions:

(lnotforallx(xeqy)to((yeqz)toforallx(yeqz)))

Proof:

Hyp Ref Line Expr
ax121(lnotforallx(xeqy)to(lnotforallx(xeqz)to((yeqz)toforallx(yeqz))))
1com12i2(lnotforallx(xeqz)to(lnotforallx(xeqy)to((yeqz)toforallx(yeqz))))
ax163(forallx(xeqz)to((yeqz)toforallx(yeqz)))
3ax14(forallx(xeqz)to(lnotforallx(xeqy)to((yeqz)toforallx(yeqz))))
2, 4casei5(lnotforallx(xeqy)to((yeqz)toforallx(yeqz)))