anass

Theorem.

Arguments:

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

Assertions:

(((phiwedgepsi)wedgechi)leftrightarrow(phiwedge(psiwedgechi)))

Proof:

Hyp Ref Line Expr
impexp1(((phiwedgepsi)tolnotchi)leftrightarrow(phito(psitolnotchi)))
im.nan2((psitolnotchi)leftrightarrowlnot(psiwedgechi))
2bi.bldim>3((phito(psitolnotchi))leftrightarrow(phitolnot(psiwedgechi)))
1, 3bitr4(((phiwedgepsi)tolnotchi)leftrightarrow(phitolnot(psiwedgechi)))
4bi.bldneg5(lnot((phiwedgepsi)tolnotchi)leftrightarrowlnot(phitolnot(psiwedgechi)))
df-an6(((phiwedgepsi)wedgechi)leftrightarrowlnot((phiwedgepsi)tolnotchi))
df-an7((phiwedge(psiwedgechi))leftrightarrowlnot(phitolnot(psiwedgechi)))
5, 6, 7<2bitr8(((phiwedgepsi)wedgechi)leftrightarrow(phiwedge(psiwedgechi)))