fv-imd

Theorem.

Arguments:

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

Hypotheses:

(phito(chitoforallxchi))
(phito(psitoforallxpsi))
(x bound in phi)

Assertions:

(phito((psitochi)toforallx(psitochi)))

Proof:

Hyp Ref Line Expr
Hypo1(phito(chitoforallxchi))
2(phito(psitoforallxpsi))
3(x bound in phi)
2, 3fv-negd4(phito(lnotpsitoforallxlnotpsi))
4com12i5(lnotpsito(phitoforallxlnotpsi))
<neg6(lnotpsito(psitochi))
6im.bldal7(forallxlnotpsitoforallx(psitochi))
5, 7rpi338(lnotpsito(phitoforallx(psitochi)))
1com12i9(chito(phitoforallxchi))
ax110(chito(psitochi))
10im.bldal11(forallxchitoforallx(psitochi))
9, 11rpi3312(chito(phitoforallx(psitochi)))
8, 12ja-pre13((psitochi)to(phitoforallx(psitochi)))
13com12i14(phito((psitochi)toforallx(psitochi)))