Theorem oridm 904

Description: Idempotent law for disjunction. Theorem *4.25 of [WhiteheadRussell] p. 117. (Contributed by NM, 11-May-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		pm1.2 903	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 902	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 209	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 206   ∨ wo 847

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 207  df-or 848

This theorem is referenced by:  pm4.25  905  orordi  928  orordir  929  nornot  1532  truortru  1578  falorfal  1581  unidm  4104  dfsn2ALT  4595  preqsnd  4808  tz7.48lem  8360  msq0i  11766  msq0d  11767  prmdvdsexp  16626  metn0  24275  rrxcph  25319  nb3grprlem2  29359  pm11.7  44437  euoreqb  47148