let Al be QC-alphabet ; :: thesis: for B being CQC-WFF-like Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
for SQ being second_Q_comp of B st B is quantifiable holds
CQCSub_All (B,SQ) is Sub_universal
let B be CQC-WFF-like Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]; :: thesis: for SQ being second_Q_comp of B st B is quantifiable holds
CQCSub_All (B,SQ) is Sub_universal
let SQ be second_Q_comp of B; :: thesis: ( B is quantifiable implies CQCSub_All (B,SQ) is Sub_universal )
assume A1: B is quantifiable ; :: thesis: CQCSub_All (B,SQ) is Sub_universal
then Sub_All (B,SQ) is Sub_universal by SUBSTUT1:14;
hence CQCSub_All (B,SQ) is Sub_universal by A1, Def5; :: thesis: verum