Theorem oridm 208

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

Assertion

Ref	Expression
oridm	⊢ ((φ ∨ φ) ↔ φ)

Proof of Theorem oridm

Step	Hyp	Ref	Expression
1		df-or 197	. 2 ⊢ ((φ ∨ φ) ↔ (¬ φ → φ))
2		pm2.24 72	. . 3 ⊢ (φ → (¬ φ → φ))
3		pm2.18 75	. . 3 ⊢ ((¬ φ → φ) → φ)
4	2, 3	impbi 139	. 2 ⊢ (φ ↔ (¬ φ → φ))
5	1, 4	bitr4 154	1 ⊢ ((φ ∨ φ) ↔ φ)

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

metamath.org