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