eqvin

Theorem.

Arguments:

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

Distinct variable conditions:

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

Assertions:

((xeqy)leftrightarrowexistsz((xeqz)wedge(zeqy)))

Proof:

Hyp Ref Line Expr
eqvini1((xeqy)toexistsz((xeqz)wedge(zeqy)))
ax17-bv2(z bound in (xeqy))
eqtr3((xeqz)to((zeqy)to(xeqy)))
3imp4(((xeqz)wedge(zeqy))to(xeqy))
2, 4imgen<i5(existsz((xeqz)wedge(zeqy))to(xeqy))
1, 5>bii6((xeqy)leftrightarrowexistsz((xeqz)wedge(zeqy)))