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 |- 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 |- q
let X be Subset of (CQC-WFF A); :: thesis: ( X |- p & {p} |- q implies X |- q )
assume that
A1: X |- p and
A2: {p} |- q ; :: thesis: X |- q
p in Cn X by A1, CQC_THE1:def 8;
then {p} c= Cn X by ZFMISC_1:31;
then A3: Cn {p} c= Cn X by CQC_THE1:15, CQC_THE1:16;
q in Cn {p} by A2, CQC_THE1:def 8;
hence X |- q by A3, CQC_THE1:def 8; :: thesis: verum