let H be ZF-formula; :: thesis: for M being non empty set
for v being Function of VAR,M st H is disjunctive holds
( M,v |= H iff ( M,v |= the_left_argument_of H or M,v |= the_right_argument_of H ) )
let M be non empty set ; :: thesis: for v being Function of VAR,M st H is disjunctive holds
( M,v |= H iff ( M,v |= the_left_argument_of H or M,v |= the_right_argument_of H ) )
let v be Function of VAR,M; :: thesis: ( H is disjunctive implies ( M,v |= H iff ( M,v |= the_left_argument_of H or M,v |= the_right_argument_of H ) ) )
assume H is disjunctive ; :: thesis: ( M,v |= H iff ( M,v |= the_left_argument_of H or M,v |= the_right_argument_of H ) )
then H = (the_left_argument_of H) 'or' (the_right_argument_of H) by ZF_LANG:41;
hence ( M,v |= H iff ( M,v |= the_left_argument_of H or M,v |= the_right_argument_of H ) ) by ZF_MODEL:17; :: thesis: verum