exan-pre

Theorem.

Arguments:

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

Hypotheses:

(existsxphiwedgepsi)

Assertions:

existsx(phiwedgepsi)

Proof:

Hyp Ref Line Expr
Hypo1(existsxphiwedgepsi)
bv-∃b2(x bound in existsxphi)
2alan>3(forallx(psiwedgeexistsxphi)leftrightarrow(forallxpsiwedgeexistsxphi))
ancom4((existsxphiwedgepsi)leftrightarrow(psiwedgeexistsxphi))
1, 4bmp>5(psiwedgeexistsxphi)
5ax-gen6forallx(psiwedgeexistsxphi)
3, 6bmp>7(forallxpsiwedgeexistsxphi)
alexan>8((forallxpsiwedgeexistsxphi)toexistsx(psiwedgephi))
7, 8ax-mp9existsx(psiwedgephi)
ancom10((psiwedgephi)leftrightarrow(phiwedgepsi))
10eqt-∃-i11(existsx(psiwedgephi)leftrightarrowexistsx(phiwedgepsi))
9, 11bmp>12existsx(phiwedgepsi)