bi.bldbi>d

Theorem.

Arguments:

phi (pr), psi (pr), chi (pr), theta (pr),

Hypotheses:

(phito(psileftrightarrowchi))

Assertions:

(phito((thetaleftrightarrowpsi)leftrightarrow(thetaleftrightarrowchi)))

Proof:

Hyp Ref Line Expr
Hypo1(phito(psileftrightarrowchi))
1bi.bldim>d2(phito((thetatopsi)leftrightarrow(thetatochi)))
2bi.bldan<d3(phito(((thetatopsi)wedge(psitotheta))leftrightarrow((thetatochi)wedge(psitotheta))))
1bi.bldim<d4(phito((psitotheta)leftrightarrow(chitotheta)))
4bi.bldan>d5(phito(((thetatochi)wedge(psitotheta))leftrightarrow((thetatochi)wedge(chitotheta))))
3, 5bitrd6(phito(((thetatopsi)wedge(psitotheta))leftrightarrow((thetatochi)wedge(chitotheta))))
dfbi7((thetaleftrightarrowpsi)leftrightarrow((thetatopsi)wedge(psitotheta)))
dfbi8((thetaleftrightarrowchi)leftrightarrow((thetatochi)wedge(chitotheta)))
6, 7, 8<2bitrg9(phito((thetaleftrightarrowpsi)leftrightarrow(thetaleftrightarrowchi)))