eqt-∃

Theorem.

Arguments:

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

Assertions:

(forallx(phileftrightarrowpsi)to(existsxphileftrightarrowexistsxpsi))

Proof:

Hyp Ref Line Expr
bi>1((phileftrightarrowpsi)to(phitopsi))
1im.bldal2(forallx(phileftrightarrowpsi)toforallx(phitopsi))
im.bldext3(forallx(phitopsi)to(existsxphitoexistsxpsi))
2, 3syl4(forallx(phileftrightarrowpsi)to(existsxphitoexistsxpsi))
bi<5((phileftrightarrowpsi)to(psitophi))
5im.bldal6(forallx(phileftrightarrowpsi)toforallx(psitophi))
im.bldext7(forallx(psitophi)to(existsxpsitoexistsxphi))
6, 7syl8(forallx(phileftrightarrowpsi)to(existsxpsitoexistsxphi))
4, 8>bid9(forallx(phileftrightarrowpsi)to(existsxphileftrightarrowexistsxpsi))