let T be Ternary_Boolean_Algebra; for a, b being Element of T holds Tern (a,b,(a `)) = b
let a, b be Element of T; Tern (a,b,(a `)) = b
Tern (a,b,(a `)) =
Tern (a,b,(Tern (b,(a `),(a `))))
by TRIDef
.=
Tern ((Tern (a,b,b)),(a `),(Tern (a,b,(a `))))
by TDis
.=
Tern (b,(a `),(Tern (a,b,(a `))))
by TRIDef
.=
Tern ((Tern (b,(a `),a)),b,(Tern (b,(a `),(a `))))
by TDis
.=
Tern ((Tern (b,(a `),((a `) `))),b,(Tern (b,(a `),(a `))))
by Lemma0
.=
Tern (b,b,(Tern (b,(a `),(a `))))
by TRADef
.=
b
by TLIDef
;
hence
Tern (a,b,(a `)) = b
; verum