let x be object ; :: thesis: for D being non empty set
for p, q being PartialPredicate of D st x in dom p & (PP_or (p,q)) . x = FALSE holds
p . x = FALSE
let D be non empty set ; :: thesis: for p, q being PartialPredicate of D st x in dom p & (PP_or (p,q)) . x = FALSE holds
p . x = FALSE
let p, q be PartialPredicate of D; :: thesis: ( x in dom p & (PP_or (p,q)) . x = FALSE implies p . x = FALSE )
assume ( x in dom p & (PP_or (p,q)) . x = FALSE ) ; :: thesis: p . x = FALSE
then p . x <> TRUE by Def4;
hence p . x = FALSE by Th3; :: thesis: verum