Theorem biorf 394

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.)

Assertion

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

Proof of Theorem biorf

Step	Hyp	Ref	Expression
1		olc 373	. 2 |- (ps -> (ph \/ ps))
2		orel1 371	. 2 |- (-. ph -> ((ph \/ ps) -> ps))
3	1, 2	impbid2 195	1 |- (-. ph -> (ps <-> (ph \/ ps)))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359

This theorem is referenced by:  biortn  395  pm5.61  693  pm5.55  867  cadan  1392  euor  2231  eueq3  3012  unineq  3506  ifor  3703  difprsnss  3847  eqtfinrelk  4487  dfphi2  4570