cbv3

Theorem.

Arguments:

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

Hypotheses:

((xeqy)to(phitopsi))
(x bound in psi)
(y bound in phi)

Assertions:

(forallxphitoforallypsi)

Proof:

Hyp Ref Line Expr
Hypo1((xeqy)to(phitopsi))
2(x bound in psi)
3(y bound in phi)
3df-Bvp4(phitoforallyphi)
4syl<5((phitophi)to(phitoforallyphi))
2df-Bvp6(psitoforallxpsi)
6ax17((phitophi)to(psitoforallxpsi))
1ax18((phitophi)to((xeqy)to(phitopsi)))
5, 7, 8cbv19(forallxforally(phitophi)to(forallxphitoforallypsi))
id10(phitophi)
10ax-gen11forally(phitophi)
11ax-gen12forallxforally(phitophi)
9, 12ax-mp13(forallxphitoforallypsi)