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  2080  eueq3dc  2947  ifordc  3611  difprsnss  3771  exmidsssn  4247  opthprc  4727  frecabcl  6487  frecsuclem  6494  swoord1  6651  indpi  7457  enq0tr  7549  mulap0r  8690  mulge0  8694  leltap  8700  ap0gt0  8715  sumsplitdc  11776  coprm  12499  gsumval2  13262  bdbl  15008  subctctexmid  15974