let F, H be Element of QC-WFF ; :: thesis: ( F is_subformula_of H implies Subformulae F c= Subformulae H )
assume A1: F is_subformula_of H ; :: thesis: Subformulae F c= Subformulae H
let a be set ; :: according to TARSKI:def 3 :: thesis: ( not a in Subformulae F or a in Subformulae H )
assume a in Subformulae F ; :: thesis: a in Subformulae H
then consider F1 being Element of QC-WFF such that
A2: F1 = a and
A3: F1 is_subformula_of F by Def23;
F1 is_subformula_of H by A1, A3, Th77;
hence a in Subformulae H by A2, Def23; :: thesis: verum