eqs5lem

Theorem.

Arguments:

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

Distinct variable conditions:

(x, y),

Assertions:

(existsx((xeqy)wedgephi)toforallx((xeqy)tophi))

Proof:

Hyp Ref Line Expr
ax111((xeqy)to(phitoforallx((xeqy)tophi)))
1imp2(((xeqy)wedgephi)toforallx((xeqy)tophi))
bv-∀b3(x bound in forallx((xeqy)tophi))
2, 3imgen<i4(existsx((xeqy)wedgephi)toforallx((xeqy)tophi))