Theorem biorfi 697

Description: A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995.)

Hypothesis

Ref	Expression
biorfi.1	|- -. ph

Assertion

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

Proof of Theorem biorfi

Step	Hyp	Ref	Expression
1		biorfi.1	. 2 |- -. ph
2		orc 665	. . 3 |- ( ps -> ( ps \/ ph ) )
3		orel2 677	. . 3 |- ( -. ph -> ( ( ps \/ ph ) -> ps ) )
4	2, 3	impbid2 141	. 2 |- ( -. ph -> ( ps <-> ( ps \/ ph ) ) )
5	1, 4	ax-mp 7	1 |- ( ps <-> ( ps \/ ph ) )

Syntax hints:   -. wn 3   <-> wb 103   \/ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 577  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm4.43  890  dn1dc  901  excxor  1309  un0  3278  opthprc  4409  frec0g  6006  dcdc  10572