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 :: thesis: for v being Function of VAR,M holds M,v |= (p '&' q) => (q '&' p)

let v be Function of VAR,M; :: thesis: M,v |= (p '&' q) => (q '&' p)
A1: ( M,v |= p & M,v |= q implies M,v |= q '&' p ) by ZF_MODEL:15;
( M,v |= p '&' q implies ( M,v |= p & M,v |= q ) ) by ZF_MODEL:15;
hence M,v |= (p '&' q) => (q '&' p) by A1, ZF_MODEL:18; :: thesis: verum

end;

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