eqvini

Theorem.

Arguments:

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

Distinct variable conditions:

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

Assertions:

((xeqy)toexistsz((xeqz)wedge(zeqy)))

Proof:

Hyp Ref Line Expr
eqtr1((zeqx)to((xeqy)to(zeqy)))
1eqcomi2((xeqz)to((xeqy)to(zeqy)))
2com12i3((xeqy)to((xeqz)to(zeqy)))
3imp4(((xeqy)wedge(xeqz))to(zeqy))
idd5((xeqy)to((xeqz)to(xeqz)))
5imp6(((xeqy)wedge(xeqz))to(xeqz))
4, 6jca7(((xeqy)wedge(xeqz))to((xeqz)wedge(zeqy)))
7exp8((xeqy)to((xeqz)to((xeqz)wedge(zeqy))))
ax17-bv9(z bound in (xeqy))
8im.bldexd10((xeqy)to(existsz(xeqz)toexistsz((xeqz)wedge(zeqy))))
ax9ex11existsz(zeqx)
eqcomi12((zeqx)to(xeqz))
12im.bldex13(existsz(zeqx)toexistsz(xeqz))
11, 13ax-mp14existsz(xeqz)
10, 14mpi15((xeqy)toexistsz((xeqz)wedge(zeqy)))