let p, q be ZF-formula; :: thesis: for M being non empty set
for v being Function of VAR,M holds
( M,v |= ('not' p) => (p => q) & M |= ('not' p) => (p => q) )
let M be non empty set ; :: thesis: for v being Function of VAR,M holds
( M,v |= ('not' p) => (p => q) & M |= ('not' p) => (p => q) )
let v be Function of VAR,M; :: thesis: ( M,v |= ('not' p) => (p => q) & M |= ('not' p) => (p => q) )

now :: thesis: for v being Function of VAR,M holds M,v |= ('not' p) => (p => q)

let v be Function of VAR,M; :: thesis: M,v |= ('not' p) => (p => q)

now :: thesis: ( M,v |= 'not' p implies M,v |= p => q )

assume M,v |= 'not' p ; :: thesis: M,v |= p => q
then not M,v |= p by ZF_MODEL:14;
hence M,v |= p => q by ZF_MODEL:18; :: thesis: verum

end;

hence M,v |= ('not' p) => (p => q) by ZF_MODEL:18; :: thesis: verum

end;

hence ( M,v |= ('not' p) => (p => q) & M |= ('not' p) => (p => q) ) ; :: thesis: verum