exdistr2

Theorem.

Arguments:

x (sv), y (sv), z (sv), phi (pr), psi (pr),

Distinct variable conditions:

(y, phi), (z, phi),

Assertions:

(existsxexistsyexistsz(phiwedgepsi)leftrightarrowexistsx(phiwedgeexistsyexistszpsi))

Proof:

Hyp Ref Line Expr
exan<vv1(existsyexistsz(phiwedgepsi)leftrightarrow(phiwedgeexistsyexistszpsi))
1eqt-∃-i2(existsxexistsyexistsz(phiwedgepsi)leftrightarrowexistsx(phiwedgeexistsyexistszpsi))