let p, q be ZF-formula; :: thesis: for M being non empty set
for v being Function of VAR ,M holds
( M,v |= (p '&' q) => (q '&' p) & M |= (p '&' q) => (q '&' p) )
let M be non empty set ; :: thesis: for v being Function of VAR ,M holds
( M,v |= (p '&' q) => (q '&' p) & M |= (p '&' q) => (q '&' p) )
let v be Function of VAR ,M; :: thesis: ( M,v |= (p '&' q) => (q '&' p) & M |= (p '&' q) => (q '&' p) )

now

let v be Function of VAR ,M; :: thesis: M,v |= (p '&' q) => (q '&' p)
( ( M,v |= p '&' q implies ( M,v |= p & M,v |= q ) ) & ( M,v |= p & M,v |= q implies M,v |= q '&' p ) ) by ZF_MODEL:15;
hence M,v |= (p '&' q) => (q '&' p) by ZF_MODEL:18; :: thesis: verum

end;

hence ( M,v |= (p '&' q) => (q '&' p) & M |= (p '&' q) => (q '&' p) ) by ZF_MODEL:def 5; :: thesis: verum