let Al be QC-alphabet ; :: thesis: for PHI being Consistent Subset of (CQC-WFF Al)

for p being Element of CQC-WFF Al holds

( PHI \/ {p} is Consistent or PHI \/ {('not' p)} is Consistent )

let PHI be Consistent Subset of (CQC-WFF Al); :: thesis: for p being Element of CQC-WFF Al holds

( PHI \/ {p} is Consistent or PHI \/ {('not' p)} is Consistent )

let p be Element of CQC-WFF Al; :: thesis: ( PHI \/ {p} is Consistent or PHI \/ {('not' p)} is Consistent )

assume ( not PHI \/ {p} is Consistent & not PHI \/ {('not' p)} is Consistent ) ; :: thesis: contradiction

then ( PHI |- 'not' p & PHI |- p ) by HENMODEL:9, HENMODEL:10;

hence contradiction by HENMODEL:def 2; :: thesis: verum

for p being Element of CQC-WFF Al holds

( PHI \/ {p} is Consistent or PHI \/ {('not' p)} is Consistent )

let PHI be Consistent Subset of (CQC-WFF Al); :: thesis: for p being Element of CQC-WFF Al holds

( PHI \/ {p} is Consistent or PHI \/ {('not' p)} is Consistent )

let p be Element of CQC-WFF Al; :: thesis: ( PHI \/ {p} is Consistent or PHI \/ {('not' p)} is Consistent )

assume ( not PHI \/ {p} is Consistent & not PHI \/ {('not' p)} is Consistent ) ; :: thesis: contradiction

then ( PHI |- 'not' p & PHI |- p ) by HENMODEL:9, HENMODEL:10;

hence contradiction by HENMODEL:def 2; :: thesis: verum