eeanv

Theorem.

Arguments:

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

Distinct variable conditions:

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

Assertions:

(existsxexistsy(phiwedgepsi)leftrightarrow(existsxphiwedgeexistsypsi))

Proof:

Hyp Ref Line Expr
exdistr1(existsxexistsy(phiwedgepsi)leftrightarrowexistsx(phiwedgeexistsypsi))
ax17-bv2(x bound in psi)
2bv-∃3(x bound in existsypsi)
3exan>4(existsx(phiwedgeexistsypsi)leftrightarrow(existsxphiwedgeexistsypsi))
1, 4bitr5(existsxexistsy(phiwedgepsi)leftrightarrow(existsxphiwedgeexistsypsi))