ax9-sv

Theorem.

Arguments:

x (sv), y (sv),

Dummy variables:

z (sv),

Distinct variable conditions:

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

Assertions:

existsx(xeqy)

Proof:

Hyp Ref Line Expr
ax9ex1existsz(zeqy)
al-ex2(forallx(xeqy)toexistsx(xeqy))
ax123(lnotforallx(xeqz)to(lnotforallx(xeqy)to((zeqy)toforallx(zeqy))))
ax164(forallx(xeqz)to((zeqy)toforallx(zeqy)))
4ax15(forallx(xeqz)to(lnotforallx(xeqy)to((zeqy)toforallx(zeqy))))
3, 5casei6(lnotforallx(xeqy)to((zeqy)toforallx(zeqy)))
bv-∀b7(x bound in forallx(xeqy))
7bv-¬8(x bound in lnotforallx(xeqy))
eqt<9((zeqx)to((zeqy)leftrightarrow(xeqy)))
9ax110(lnotforallx(xeqy)to((zeqx)to((zeqy)leftrightarrow(xeqy))))
6, 8, 10cbvexd-dv11(lnotforallx(xeqy)to(existsz(zeqy)leftrightarrowexistsx(xeqy)))
1, 11bmpi>12(lnotforallx(xeqy)toexistsx(xeqy))
2, 12casei13existsx(xeqy)

Theorems:

NameComment
cbv1-dv
cbv2-dv
cbval-dv
cbvald-dv
cbvexd-dv