Theorem biorfi 396

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 374	. . 3 |- (ps -> (ps \/ ph))
3		orel2 372	. . 3 |- (-. ph -> ((ps \/ ph) -> ps))
4	2, 3	impbid2 195	. 2 |- (-. ph -> (ps <-> (ps \/ ph)))
5	1, 4	ax-mp 5	1 |- (ps <-> (ps \/ ph))

Syntax hints:  -. wn 3   <-> wb 176   \/ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359

This theorem is referenced by:  pm4.43  893  dn1  932  indifdir  3512  un0  3576  eqtfinrelk  4487  proj1op  4601  proj2op  4602  imadif  5172