exan>vvv

Theorem.

Arguments:

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

Distinct variable conditions:

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

Assertions:

(existsxexistsyexistsz(phiwedgepsi)leftrightarrow(existsxexistsyexistszphiwedgepsi))

Proof:

Hyp Ref Line Expr
exan>vv1(existsyexistsz(phiwedgepsi)leftrightarrow(existsyexistszphiwedgepsi))
1eqt-∃-i2(existsxexistsyexistsz(phiwedgepsi)leftrightarrowexistsx(existsyexistszphiwedgepsi))
exan>3(existsx(existsyexistszphiwedgepsi)leftrightarrow(existsxexistsyexistszphiwedgepsi))
2, 3bitr4(existsxexistsyexistsz(phiwedgepsi)leftrightarrow(existsxexistsyexistszphiwedgepsi))