eeor

Theorem.

Arguments:

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

Hypotheses:

(x bound in psi)
(y bound in phi)

Assertions:

(existsxexistsy(phiveepsi)leftrightarrow(existsxphiveeexistsypsi))

Proof:

Hyp Ref Line Expr
Hypo1(x bound in psi)
2(y bound in phi)
2exor<3(existsy(phiveepsi)leftrightarrow(phiveeexistsypsi))
3eqt-∃-i4(existsxexistsy(phiveepsi)leftrightarrowexistsx(phiveeexistsypsi))
1bv-∃5(x bound in existsypsi)
5exor>6(existsx(phiveeexistsypsi)leftrightarrow(existsxphiveeexistsypsi))
4, 6bitr7(existsxexistsy(phiveepsi)leftrightarrow(existsxphiveeexistsypsi))