∃1→∃

Theorem.

Arguments:

x (sv), phi (pr),

Dummy variables:

y (sv),

Distinct variable conditions:

(y, x), (y, phi),

Assertions:

(_e1xphitoexistsxphi)

Proof:

Hyp Ref Line Expr
ax17-bv1(y bound in phi)
1df-∃1-alt12(_e1xphileftrightarrowexistsx(phiwedgeforally([y/x]phito(xeqy))))
ex.andi3(existsx(phiwedgeforally([y/x]phito(xeqy)))to(existsxphiwedgeexistsxforally([y/x]phito(xeqy))))
2, 3brpi214(_e1xphito(existsxphiwedgeexistsxforally([y/x]phito(xeqy))))
4siman<5(_e1xphitoexistsxphi)