Theorem biorfi 747

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 713	. . 3 |- ( ps -> ( ps \/ ph ) )
3		orel2 727	. . 3 |- ( -. ph -> ( ( ps \/ ph ) -> ps ) )
4	2, 3	impbid2 143	. 2 |- ( -. ph -> ( ps <-> ( ps \/ ph ) ) )
5	1, 4	ax-mp 5	1 |- ( ps <-> ( ps \/ ph ) )

Syntax hints:   -. wn 3   <-> wb 105   \/ wo 709

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 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm4.43  951  dn1dc  962  excxor  1389  un0  3485  opthprc  4715  frec0g  6464  nninfwlporlemd  7247  gsum0g  13098  if0ab  15535