cbval-dv

Theorem.

Arguments:

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

Distinct variable conditions:

(x, y), (z, x), (z, y),

Hypotheses:

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

Assertions:

(forallxphileftrightarrowforallypsi)

Proof:

Hyp Ref Line Expr
Hypo1((xeqy)to(phileftrightarrowpsi))
2(x bound in psi)
3(y bound in phi)
3df-Bvp4(phitoforallyphi)
2df-Bvp5(psitoforallxpsi)
4syl<6((phitophi)to(phitoforallyphi))
5ax17((phitophi)to(psitoforallxpsi))
1ax18((phitophi)to((xeqy)to(phileftrightarrowpsi)))
6, 7, 8cbv2-dv9(forallxforally(phitophi)to(forallxphileftrightarrowforallypsi))
id10(phitophi)
10ax-gen11forally(phitophi)
11ax-gen12forallxforally(phitophi)
9, 12ax-mp13(forallxphileftrightarrowforallypsi)