Theorem biorfi 665

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 633	. . 3 |- ( ps -> ( ps \/ ph ) )
3		orel2 645	. . 3 |- ( -. ph -> ( ( ps \/ ph ) -> ps ) )
4	2, 3	impbid2 131	. 2 |- ( -. ph -> ( ps <-> ( ps \/ ph ) ) )
5	1, 4	ax-mp 7	1 |- ( ps <-> ( ps \/ ph ) )

Syntax hints:   -. wn 3   <-> wb 98   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  pm4.43  856  dn1dc  867  excxor  1269  un0  3251  opthprc  4391  frec0g  5983  dcdc  9901