Metamath Proof Explorer


Theorem biorf

Description: A wff is equivalent to its disjunction with falsehood. Theorem *4.74 of WhiteheadRussell p. 121. (Contributed by NM, 23-Mar-1995) (Proof shortened by Wolf Lammen, 18-Nov-2012)

Ref Expression
Assertion biorf
|- ( -. ph -> ( ps <-> ( ph \/ ps ) ) )

Proof

Step Hyp Ref Expression
1 olc
 |-  ( ps -> ( ph \/ ps ) )
2 orel1
 |-  ( -. ph -> ( ( ph \/ ps ) -> ps ) )
3 1 2 impbid2
 |-  ( -. ph -> ( ps <-> ( ph \/ ps ) ) )