DEFINITION and3_ind()
TYPE =
∀P0:Prop.∀P1:Prop.∀P2:Prop.∀P:Prop.(P0→P1→P2→P)→(and3 P0 P1 P2)→P
BODY =
assume P0: Prop
assume P1: Prop
assume P2: Prop
assume P: Prop
suppose H: P0→P1→P2→P
suppose H1: and3 P0 P1 P2
by cases on H1 we prove P
case and3_intro H2:P0 H3:P1 H4:P2 ⇒
the thesis becomes P
by (H H2 H3 H4)
P
we proved P
we proved ∀P0:Prop.∀P1:Prop.∀P2:Prop.∀P:Prop.(P0→P1→P2→P)→(and3 P0 P1 P2)→P