sb-eqat<x

Theorem.

Arguments:

y (sv), x (sv),

Dummy variables:

z (sv),

Distinct variable conditions:

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

Assertions:

[y/x](xeqy)

Proof:

Hyp Ref Line Expr
eqid1(yeqy)
1eqvini-sv2existsz((yeqz)wedge(zeqy))
eqcomi3((yeqz)to(zeqy))
3im.bldan<4(((yeqz)wedge(zeqy))to((zeqy)wedge(zeqy)))
2, 4im.bldex5existsz((zeqy)wedge(zeqy))
eqvini-sv6((zeqy)toexistsx((zeqx)wedge(xeqy)))
eqcomi7((zeqx)to(xeqz))
7im.bldan<8(((zeqx)wedge(xeqy))to((xeqz)wedge(xeqy)))
6, 8im.bldex9((zeqy)toexistsx((xeqz)wedge(xeqy)))
9im.bldan>10(((zeqy)wedge(zeqy))to((zeqy)wedgeexistsx((xeqz)wedge(xeqy))))
5, 10im.bldex11existsz((zeqy)wedgeexistsx((xeqz)wedge(xeqy)))
11df-sb12[y/x](xeqy)