Theorem oridm 208

Description: Idempotent law for disjunction. Theorem *4.25 of [WhiteheadRussell] p. 117.

Assertion

Ref	Expression
oridm	|- ((ph \/ ph) <-> ph)

Proof of Theorem oridm

Step	Hyp	Ref	Expression
1		df-or 197	. 2 |- ((ph \/ ph) <-> (-. ph -> ph))
2		pm2.24 72	. . 3 |- (ph -> (-. ph -> ph))
3		pm2.18 75	. . 3 |- ((-. ph -> ph) -> ph)
4	2, 3	impbi 139	. 2 |- (ph <-> (-. ph -> ph))
5	1, 4	bitr4 154	1 |- ((ph \/ ph) <-> ph)

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127   \/ wo 195

This theorem is referenced by:  orordi 222  orordir 223  unidm 1603  elsncg 1825  ordtri3or 2230  suceloni 2314  tz7.48lem 2993  sq0 4211

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

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