im.bidian

Theorem.

Arguments:

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

Assertions:

((phito(psileftrightarrowchi))leftrightarrow((phiwedgepsi)leftrightarrow(phiwedgechi)))

Proof:

Hyp Ref Line Expr
conb1((psileftrightarrowchi)leftrightarrow(lnotpsileftrightarrowlnotchi))
1bi.bldim>2((phito(psileftrightarrowchi))leftrightarrow(phito(lnotpsileftrightarrowlnotchi)))
im.bidi3((phito(lnotpsileftrightarrowlnotchi))leftrightarrow((phitolnotpsi)leftrightarrow(phitolnotchi)))
conb4(((phitolnotpsi)leftrightarrow(phitolnotchi))leftrightarrow(lnot(phitolnotpsi)leftrightarrowlnot(phitolnotchi)))
2, 3, 42bitr5((phito(psileftrightarrowchi))leftrightarrow(lnot(phitolnotpsi)leftrightarrowlnot(phitolnotchi)))
df-an6((phiwedgepsi)leftrightarrowlnot(phitolnotpsi))
df-an7((phiwedgechi)leftrightarrowlnot(phitolnotchi))
6, 7bi.bldbi<>8(((phiwedgepsi)leftrightarrow(phiwedgechi))leftrightarrow(lnot(phitolnotpsi)leftrightarrowlnot(phitolnotchi)))
5, 8><bitr9((phito(psileftrightarrowchi))leftrightarrow((phiwedgepsi)leftrightarrow(phiwedgechi)))