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 holds J |= (p '&' q) => (q '&' p)
let A be non empty set ; :: thesis: for p, q being Element of CQC-WFF Al
for J being interpretation of Al,A holds J |= (p '&' q) => (q '&' p)
let p, q be Element of CQC-WFF Al; :: thesis: for J being interpretation of Al,A holds J |= (p '&' q) => (q '&' p)
let J be interpretation of Al,A; :: thesis: J |= (p '&' q) => (q '&' p)
let v be Element of Valuations_in (Al,A); :: according to VALUAT_1:def 8 :: thesis: J,v |= (p '&' q) => (q '&' p)
thus J,v |= (p '&' q) => (q '&' p) by Th33; :: thesis: verum