let q, p be Element of CQC-WFF ; :: thesis: for x being bound_QC-variable st not x in still_not-bound_in q holds
((Ex (x,p)) => q) <=> (All (x,(p => q))) is valid
let x be bound_QC-variable; :: thesis: ( not x in still_not-bound_in q implies ((Ex (x,p)) => q) <=> (All (x,(p => q))) is valid )
assume not x in still_not-bound_in q ; :: thesis: ((Ex (x,p)) => q) <=> (All (x,(p => q))) is valid
then ( ((Ex (x,p)) => q) => (All (x,(p => q))) is valid & (All (x,(p => q))) => ((Ex (x,p)) => q) is valid ) by Th84;
hence ((Ex (x,p)) => q) <=> (All (x,(p => q))) is valid by Lm14; :: thesis: verum