an.ordi<

Theorem.

Arguments:

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

Assertions:

((phiwedge(psiveechi))leftrightarrow((phiwedgepsi)vee(phiwedgechi)))

Proof:

Hyp Ref Line Expr
or.andi<1((lnotphivee(lnotpsiwedgelnotchi))leftrightarrow((lnotphiveelnotpsi)wedge(lnotphiveelnotchi)))
nor.an2(lnot(psiveechi)leftrightarrow(lnotpsiwedgelnotchi))
2bi.bldor>3((lnotphiveelnot(psiveechi))leftrightarrow(lnotphivee(lnotpsiwedgelnotchi)))
nan.or4(lnot(phiwedgepsi)leftrightarrow(lnotphiveelnotpsi))
nan.or5(lnot(phiwedgechi)leftrightarrow(lnotphiveelnotchi))
4, 5bi.bldan<>6((lnot(phiwedgepsi)wedgelnot(phiwedgechi))leftrightarrow((lnotphiveelnotpsi)wedge(lnotphiveelnotchi)))
1, 3, 6<2bitr7((lnotphiveelnot(psiveechi))leftrightarrow(lnot(phiwedgepsi)wedgelnot(phiwedgechi)))
7bi.bldneg8(lnot(lnotphiveelnot(psiveechi))leftrightarrowlnot(lnot(phiwedgepsi)wedgelnot(phiwedgechi)))
an.or9((phiwedge(psiveechi))leftrightarrowlnot(lnotphiveelnot(psiveechi)))
or.an10(((phiwedgepsi)vee(phiwedgechi))leftrightarrowlnot(lnot(phiwedgepsi)wedgelnot(phiwedgechi)))
8, 9, 10<2bitr11((phiwedge(psiveechi))leftrightarrow((phiwedgepsi)vee(phiwedgechi)))