19.25

Theorem.

Arguments:

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

Assertions:

(forallyexistsx(phitopsi)to(existsyforallxphitoexistsyexistsxpsi))

Proof:

Hyp Ref Line Expr
bexim1(existsx(phitopsi)leftrightarrow(forallxphitoexistsxpsi))
1bi>2(existsx(phitopsi)to(forallxphitoexistsxpsi))
2im.bldal3(forallyexistsx(phitopsi)toforally(forallxphitoexistsxpsi))
im.bldext4(forally(forallxphitoexistsxpsi)to(existsyforallxphitoexistsyexistsxpsi))
3, 4syl5(forallyexistsx(phitopsi)to(existsyforallxphitoexistsyexistsxpsi))