let A be QC-alphabet ; :: thesis: for G, H being Element of QC-WFF A st G is_subformula_of H & H is_subformula_of G holds
G = H
let G, H be Element of QC-WFF A; :: thesis: ( G is_subformula_of H & H is_subformula_of G implies G = H )
assume that
A1: G is_subformula_of H and
A2: H is_subformula_of G ; :: thesis: G = H
assume A3: G <> H ; :: thesis: contradiction
then G is_proper_subformula_of H by A1;
then A4: len (@ G) < len (@ H) by Th54;
H is_proper_subformula_of G by A2, A3;
hence contradiction by A4, Th54; :: thesis: verum