let x be bound_QC-variable; :: thesis: for p being Element of QC-WFF holds
( All x,p is Element of CQC-WFF iff p is Element of CQC-WFF )
let p be Element of QC-WFF ; :: thesis: ( All x,p is Element of CQC-WFF iff p is Element of CQC-WFF )
thus ( All x,p is Element of CQC-WFF implies p is Element of CQC-WFF ) :: thesis: ( p is Element of CQC-WFF implies All x,p is Element of CQC-WFF )

proof

assume A1: All x,p is Element of CQC-WFF ; :: thesis: p is Element of CQC-WFF
then Fixed (All x,p) = {} by Th13;
then A2: Fixed p = {} by QC_LANG3:81;
Free (All x,p) = {} by A1, Th13;
then Free p = {} by QC_LANG3:70;
hence p is Element of CQC-WFF by A2, Th13; :: thesis: verum

end;

assume A3: p is Element of CQC-WFF ; :: thesis: All x,p is Element of CQC-WFF
then Fixed p = {} by Th13;
then A4: Fixed (All x,p) = {} by QC_LANG3:81;
Free p = {} by A3, Th13;
then Free (All x,p) = {} by QC_LANG3:70;
hence All x,p is Element of CQC-WFF by A4, Th13; :: thesis: verum