Theorem biorfi 552

Description: A wff is equivalent to its disjunction with falsehood.

Hypothesis

Ref	Expression
biorfi.1	|- -. ph

Assertion

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

Proof of Theorem biorfi

Step	Hyp	Ref	Expression
1		biorfi.1	. . 3 |- -. ph
2		biorf 551	. . 3 |- (-. ph -> (ps <-> (ph \/ ps)))
3	1, 2	ax-mp 6	. 2 |- (ps <-> (ph \/ ps))
4		orcom 209	. 2 |- ((ph \/ ps) <-> (ps \/ ph))
5	3, 4	bitr 151	1 |- (ps <-> (ps \/ ph))

Syntax hints:  -. wn 1   <-> wb 127   \/ wo 195

This theorem is referenced by:  un0 1721  opthprc 2457  imadif 2714

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198

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