let x be bound_QC-variable; :: thesis: for p being QC-formula st p is closed holds
All (x,p) is closed
let p be QC-formula; :: thesis: ( p is closed implies All (x,p) is closed )
assume still_not-bound_in p = {} ; :: according to QC_LANG1:def 29 :: thesis: All (x,p) is closed
then still_not-bound_in p c= {x} by XBOOLE_1:2;
hence All (x,p) is closed by Th27; :: thesis: verum