an.ordi>

Theorem.

Arguments:

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

Assertions:

(((phiveepsi)wedgechi)leftrightarrow((phiwedgechi)vee(psiwedgechi)))

Proof:

Hyp Ref Line Expr
ancom1(((phiveepsi)wedgechi)leftrightarrow(chiwedge(phiveepsi)))
an.ordi<2((chiwedge(phiveepsi))leftrightarrow((chiwedgephi)vee(chiwedgepsi)))
1, 2bitr3(((phiveepsi)wedgechi)leftrightarrow((chiwedgephi)vee(chiwedgepsi)))
ancom4((chiwedgephi)leftrightarrow(phiwedgechi))
ancom5((chiwedgepsi)leftrightarrow(psiwedgechi))
4, 5bi.bldor<>6(((chiwedgephi)vee(chiwedgepsi))leftrightarrow((phiwedgechi)vee(psiwedgechi)))
3, 6bitr7(((phiveepsi)wedgechi)leftrightarrow((phiwedgechi)vee(psiwedgechi)))