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

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

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

end;

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