fv-im

Theorem.

Arguments:

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

Hypotheses:

(psitoforallxpsi)
(phitoforallxphi)

Assertions:

((phitopsi)toforallx(phitopsi))

Proof:

Hyp Ref Line Expr
Hypo1(psitoforallxpsi)
2(phitoforallxphi)
2fv-neg3(lnotphitoforallxlnotphi)
<neg4(lnotphito(phitopsi))
4im.bldal5(forallxlnotphitoforallx(phitopsi))
3, 5syl6(lnotphitoforallx(phitopsi))
ax17(psito(phitopsi))
7im.bldal8(forallxpsitoforallx(phitopsi))
1, 8syl9(psitoforallx(phitopsi))
6, 9ja-pre10((phitopsi)toforallx(phitopsi))