cbvald

Theorem.

Arguments:

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

Distinct variable conditions:

(x, phi), (x, chi),

Hypotheses:

(phito((xeqy)to(psileftrightarrowchi)))
(phito(psitoforallypsi))
(y bound in phi)

Assertions:

(phito(forallxpsileftrightarrowforallychi))

Proof:

Hyp Ref Line Expr
Hypo1(phito((xeqy)to(psileftrightarrowchi)))
2(phito(psitoforallypsi))
3(y bound in phi)
2, 3fv-imt4((phitopsi)toforally(phitopsi))
4df-Bvp5(y bound in (phitopsi))
ax17-bv6(x bound in (phitochi))
1com12i7((xeqy)to(phito(psileftrightarrowchi)))
7im.bidi8((xeqy)to((phitopsi)leftrightarrow(phitochi)))
5, 6, 8cbval9(forallx(phitopsi)leftrightarrowforally(phitochi))
imgen>10(forallx(phitopsi)leftrightarrow(phitoforallxpsi))
3imgen>11(forally(phitochi)leftrightarrow(phitoforallychi))
9, 10, 11>2bitr12((phitoforallxpsi)leftrightarrow(phitoforallychi))
12im.bidi13(phito(forallxpsileftrightarrowforallychi))