Theorem biorf 746

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 713	. 2 |- ( ps -> ( ph \/ ps ) )
2		orel1 727	. 2 |- ( -. ph -> ( ( ph \/ ps ) -> ps ) )
3	1, 2	impbid2 143	1 |- ( -. ph -> ( ps <-> ( ph \/ ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 105   \/ wo 710

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 616  ax-io 711

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  biortn  747  pm5.61  796  pm5.55dc  915  3bior1fd  1364  3bior2fd  1366  euor  2081  eueq3dc  2954  ifordc  3621  difprsnss  3782  exmidsssn  4262  opthprc  4744  frecabcl  6508  frecsuclem  6515  swoord1  6672  indpi  7490  enq0tr  7582  mulap0r  8723  mulge0  8727  leltap  8733  ap0gt0  8748  sumsplitdc  11858  coprm  12581  gsumval2  13344  bdbl  15090  subctctexmid  16139