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 holds
X |- (p => q) => q
let p, q be Element of CQC-WFF A; :: thesis: for X being Subset of (CQC-WFF A) st X |- p holds
X |- (p => q) => q
let X be Subset of (CQC-WFF A); :: thesis: ( X |- p implies X |- (p => q) => q )
assume A1: X |- p ; :: thesis: X |- (p => q) => q
X |- p => ((p => q) => q) by CQC_THE1:59;
hence X |- (p => q) => q by A1, CQC_THE1:55; :: thesis: verum