let A be QC-alphabet ; for p, q being Element of CQC-WFF A
for x being bound_QC-variable of A st All (x,(p => q)) is valid holds
(Ex (x,p)) => (Ex (x,q)) is valid
let p, q be Element of CQC-WFF A; for x being bound_QC-variable of A st All (x,(p => q)) is valid holds
(Ex (x,p)) => (Ex (x,q)) is valid
let x be bound_QC-variable of A; ( All (x,(p => q)) is valid implies (Ex (x,p)) => (Ex (x,q)) is valid )
assume A1:
All (x,(p => q)) is valid
; (Ex (x,p)) => (Ex (x,q)) is valid
(All (x,(p => q))) => ((Ex (x,p)) => (Ex (x,q))) is valid
by Th34;
hence
(Ex (x,p)) => (Ex (x,q)) is valid
by A1, CQC_THE1:65; verum