ax9alt

Theorem.

Arguments:

x (sv), y (st), phi (pr),

Distinct variable conditions:

(x, y),

Assertions:

(forallx((xeqy)toforallxphi)tophi)

Proof:

Hyp Ref Line Expr
ax91lnotforallxlnot(xeqy)
df-ex2(existsx(xeqy)leftrightarrowlnotforallxlnot(xeqy))
1, 2bmp<3existsx(xeqy)
im.bldext4(forallx((xeqy)toforallxphi)to(existsx(xeqy)toexistsxforallxphi))
3, 4mpi5(forallx((xeqy)toforallxphi)toexistsxforallxphi)
ax6e6(existsxforallxphitophi)
5, 6syl7(forallx((xeqy)toforallxphi)tophi)