Theorem oridm 500

Description: Idempotent law for disjunction. Theorem *4.25 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 16-Apr-2011.) (Proof shortened by Wolf Lammen, 10-Mar-2013.)

Assertion

Ref	Expression
oridm	⊢ ((φ ∨ φ) ↔ φ)

Proof of Theorem oridm

Step	Hyp	Ref	Expression
1		pm1.2 499	. 2 ⊢ ((φ ∨ φ) → φ)
2		pm2.07 385	. 2 ⊢ (φ → (φ ∨ φ))
3	1, 2	impbii 180	1 ⊢ ((φ ∨ φ) ↔ φ)

Syntax hints:   ↔ 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:  pm4.25  501  orordi  516  orordir  517  truortru  1340  falorfal  1343  unidm  3408