cbv1

Theorem.

Arguments:

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

Hypotheses:

(phito((xeqy)to(psitochi)))
(phito(chitoforallxchi))
(phito(psitoforallypsi))

Assertions:

(forallxforallyphito(forallxpsitoforallychi))

Proof:

Hyp Ref Line Expr
Hypo1(phito((xeqy)to(psitochi)))
2(phito(chitoforallxchi))
3(phito(psitoforallypsi))
ax44(forallyphitophi)
3, 4syl5(forallyphito(psitoforallypsi))
52im.bldal6(forallxforallyphito(forallxpsitoforallxforallypsi))
ax77(forallxforallypsitoforallyforallxpsi)
6, 7rpi338(forallxforallyphito(forallxpsitoforallyforallxpsi))
1com23i9(phito(psito((xeqy)tochi)))
2, 9rpi33d10(phito(psito((xeqy)toforallxchi)))
102im.bldal11(forallxphito(forallxpsitoforallx((xeqy)toforallxchi)))
ax9alt-sv12(forallx((xeqy)toforallxchi)tochi)
11, 12rpi3313(forallxphito(forallxpsitochi))
132im.bldal14(forallyforallxphito(forallyforallxpsitoforallychi))
ax715(forallxforallyphitoforallyforallxphi)
14, 15syl16(forallxforallyphito(forallyforallxpsitoforallychi))
8, 16syld17(forallxforallyphito(forallxpsitoforallychi))