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

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

X |- p => r

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

X |- p => r

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

assume X |- p => (q => r) ; :: thesis: ( not X |- p => q or X |- p => r )

then X |- (p => q) => (p => r) by Th67;

hence ( not X |- p => q or X |- p => r ) by CQC_THE1:55; :: thesis: verum

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

X |- p => r

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

X |- p => r

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

assume X |- p => (q => r) ; :: thesis: ( not X |- p => q or X |- p => r )

then X |- (p => q) => (p => r) by Th67;

hence ( not X |- p => q or X |- p => r ) by CQC_THE1:55; :: thesis: verum