let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A
for x being bound_QC-variable of A holds (Ex (x,(p => q))) <=> ((All (x,p)) => (Ex (x,q))) is valid
let p, q be Element of CQC-WFF A; :: thesis: for x being bound_QC-variable of A holds (Ex (x,(p => q))) <=> ((All (x,p)) => (Ex (x,q))) is valid
let x be bound_QC-variable of A; :: thesis: (Ex (x,(p => q))) <=> ((All (x,p)) => (Ex (x,q))) is valid
( (Ex (x,(p => q))) => ((All (x,p)) => (Ex (x,q))) is valid & ((All (x,p)) => (Ex (x,q))) => (Ex (x,(p => q))) is valid ) by Th61;
hence (Ex (x,(p => q))) <=> ((All (x,p)) => (Ex (x,q))) is valid by Lm14; :: thesis: verum