19.38

Theorem.

Arguments:

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

Assertions:

((existsxphitoforallxpsi)toforallx(phitopsi))

Proof:

Hyp Ref Line Expr
bv-∃b1(x bound in existsxphi)
bv-∀b2(x bound in forallxpsi)
1, 2bv-→3(x bound in (existsxphitoforallxpsi))
spec-ex4(phitoexistsxphi)
ax45(forallxpsitopsi)
4, 5syl346((existsxphitoforallxpsi)to(phitopsi))
3, 6imgen>i7((existsxphitoforallxpsi)toforallx(phitopsi))