let F be Ternary-Field; :: thesis: for a, x, b, x9 being Scalar of F st a <> 0. F & Tern a,x,b = Tern a,x9,b holds
x = x9
let a, x, b, x9 be Scalar of F; :: thesis: ( a <> 0. F & Tern a,x,b = Tern a,x9,b implies x = x9 )
assume that
A1: a <> 0. F and
A2: Tern a,x,b = Tern a,x9,b ; :: thesis: x = x9
set c = Tern a,x,b;
A3: Tern a,x,b = Tern (0. F),x,(Tern a,x,b) by Def7;
Tern a,x9,b = Tern (0. F),x9,(Tern a,x,b) by A2, Def7;
hence x = x9 by A1, A3, Def7; :: thesis: verum