ee4anv

Theorem.

Arguments:

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

Distinct variable conditions:

(z, phi), (w, phi), (x, psi), (y, psi), (y, z), (x, w),

Assertions:

(existsxexistsyexistszexistsw(phiwedgepsi)leftrightarrow(existsxexistsyphiwedgeexistszexistswpsi))

Proof:

Hyp Ref Line Expr
excom1(existsyexistszexistsw(phiwedgepsi)leftrightarrowexistszexistsyexistsw(phiwedgepsi))
1eqt-∃-i2(existsxexistsyexistszexistsw(phiwedgepsi)leftrightarrowexistsxexistszexistsyexistsw(phiwedgepsi))
eeanv3(existsyexistsw(phiwedgepsi)leftrightarrow(existsyphiwedgeexistswpsi))
3eqt-∃-i4(existszexistsyexistsw(phiwedgepsi)leftrightarrowexistsz(existsyphiwedgeexistswpsi))
4eqt-∃-i5(existsxexistszexistsyexistsw(phiwedgepsi)leftrightarrowexistsxexistsz(existsyphiwedgeexistswpsi))
eeanv6(existsxexistsz(existsyphiwedgeexistswpsi)leftrightarrow(existsxexistsyphiwedgeexistszexistswpsi))
2, 5, 62bitr7(existsxexistsyexistszexistsw(phiwedgepsi)leftrightarrow(existsxexistsyphiwedgeexistszexistswpsi))