fv-bid

Theorem.

Arguments:

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

Hypotheses:

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

Assertions:

(phito((psileftrightarrowchi)toforallx(psileftrightarrowchi)))

Proof:

Hyp Ref Line Expr
Hypo1(phito(chitoforallxchi))
2(phito(psitoforallxpsi))
3(x bound in phi)
1, 2, 3fv-imd4(phito((psitochi)toforallx(psitochi)))
1, 2, 3fv-imd5(phito((chitopsi)toforallx(chitopsi)))
4, 5im.bldan<>d6(phito(((psitochi)wedge(chitopsi))to(forallx(psitochi)wedgeforallx(chitopsi))))
dfbi7((psileftrightarrowchi)leftrightarrow((psitochi)wedge(chitopsi)))
al.dfbi8(forallx(psileftrightarrowchi)leftrightarrow(forallx(psitochi)wedgeforallx(chitopsi)))
6, 7, 8<imtrg9(phito((psileftrightarrowchi)toforallx(psileftrightarrowchi)))