let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A

for X being Subset of (CQC-WFF A) st X |- p => (p => q) holds

X |- p => q

let p, q be Element of CQC-WFF A; :: thesis: for X being Subset of (CQC-WFF A) st X |- p => (p => q) holds

X |- p => q

let X be Subset of (CQC-WFF A); :: thesis: ( X |- p => (p => q) implies X |- p => q )

assume A1: X |- p => (p => q) ; :: thesis: X |- p => q

X |- (p => (p => q)) => (p => q) by CQC_THE1:59;

hence X |- p => q by A1, CQC_THE1:55; :: thesis: verum

for X being Subset of (CQC-WFF A) st X |- p => (p => q) holds

X |- p => q

let p, q be Element of CQC-WFF A; :: thesis: for X being Subset of (CQC-WFF A) st X |- p => (p => q) holds

X |- p => q

let X be Subset of (CQC-WFF A); :: thesis: ( X |- p => (p => q) implies X |- p => q )

assume A1: X |- p => (p => q) ; :: thesis: X |- p => q

X |- (p => (p => q)) => (p => q) by CQC_THE1:59;

hence X |- p => q by A1, CQC_THE1:55; :: thesis: verum