or.andi<

Theorem.

Arguments:

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

Assertions:

((phivee(psiwedgechi))leftrightarrow((phiveepsi)wedge(phiveechi)))

Proof:

Hyp Ref Line Expr
siman<1((psiwedgechi)topsi)
1im.bldor>2((phivee(psiwedgechi))to(phiveepsi))
siman>3((psiwedgechi)tochi)
3im.bldor>4((phivee(psiwedgechi))to(phiveechi))
2, 4jca5((phivee(psiwedgechi))to((phiveepsi)wedge(phiveechi)))
>andc6((lnotphitopsi)to((lnotphitochi)to(lnotphito(psiwedgechi))))
df-or7((phiveechi)leftrightarrow(lnotphitochi))
df-or8((phivee(psiwedgechi))leftrightarrow(lnotphito(psiwedgechi)))
6, 7, 8<imtrg9((lnotphitopsi)to((phiveechi)to(phivee(psiwedgechi))))
df-or10((phiveepsi)leftrightarrow(lnotphitopsi))
9, 10brpi2111((phiveepsi)to((phiveechi)to(phivee(psiwedgechi))))
11imp12(((phiveepsi)wedge(phiveechi))to(phivee(psiwedgechi)))
5, 12>bii13((phivee(psiwedgechi))leftrightarrow((phiveepsi)wedge(phiveechi)))