imgen<

Theorem.

Arguments:

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

Hypotheses:

(x bound in psi)

Assertions:

(forallx(phitopsi)leftrightarrow(existsxphitopsi))

Proof:

Hyp Ref Line Expr
Hypo1(x bound in psi)
im.bldext2(forallx(phitopsi)to(existsxphitoexistsxpsi))
1fv.eqex3(psileftrightarrowexistsxpsi)
2, 3brpi33<4(forallx(phitopsi)to(existsxphitopsi))
bv-∃b5(x bound in existsxphi)
1, 5bv-→6(x bound in (existsxphitopsi))
spec-ex7(phitoexistsxphi)
7syl>8((existsxphitopsi)to(phitopsi))
6, 8imgen>i9((existsxphitopsi)toforallx(phitopsi))
4, 9>bii10(forallx(phitopsi)leftrightarrow(existsxphitopsi))