let B be Element of [:QC-Sub-WFF,bound_QC-variables:]; :: thesis: for SQ being second_Q_comp of B st B is quantifiable holds
Sub_the_scope_of (Sub_All (B,SQ)) = B `1
let SQ be second_Q_comp of B; :: thesis: ( B is quantifiable implies Sub_the_scope_of (Sub_All (B,SQ)) = B `1 )
assume A1: B is quantifiable ; :: thesis: Sub_the_scope_of (Sub_All (B,SQ)) = B `1
then Sub_All (B,SQ) is Sub_universal by Th14;
hence Sub_the_scope_of (Sub_All (B,SQ)) = B `1 by A1, Def34; :: thesis: verum