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_All (B,SQ)) `1 = All ((B `2),((B `1) `1)) & (Sub_All (B,SQ)) `2 = SQ )
let SQ be second_Q_comp of B; :: thesis: ( B is quantifiable implies ( (Sub_All (B,SQ)) `1 = All ((B `2),((B `1) `1)) & (Sub_All (B,SQ)) `2 = SQ ) )
assume B is quantifiable ; :: thesis: ( (Sub_All (B,SQ)) `1 = All ((B `2),((B `1) `1)) & (Sub_All (B,SQ)) `2 = SQ )
then Sub_All (B,SQ) = [(All ((B `2),((B `1) `1))),SQ] by SUBSTUT1:def 24;
hence ( (Sub_All (B,SQ)) `1 = All ((B `2),((B `1) `1)) & (Sub_All (B,SQ)) `2 = SQ ) by MCART_1:7; :: thesis: verum