let Al be QC-alphabet ; :: thesis: for A being non empty set
for p, q being Element of CQC-WFF Al
for J being interpretation of Al,A st J |= p & J |= p => q holds
J |= q
let A be non empty set ; :: thesis: for p, q being Element of CQC-WFF Al
for J being interpretation of Al,A st J |= p & J |= p => q holds
J |= q
let p, q be Element of CQC-WFF Al; :: thesis: for J being interpretation of Al,A st J |= p & J |= p => q holds
J |= q
let J be interpretation of Al,A; :: thesis: ( J |= p & J |= p => q implies J |= q )
assume A1: ( J |= p & J |= p => q ) ; :: thesis: J |= q

now :: thesis: for v being Element of Valuations_in (Al,A) holds J,v |= q

let v be Element of Valuations_in (Al,A); :: thesis: J,v |= q
( J,v |= p & J,v |= p => q ) by A1;
hence J,v |= q by Th24; :: thesis: verum

end;

hence J |= q ; :: thesis: verum