Theorem oridm 905

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		pm1.2 904	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 903	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 209	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 206   ∨ wo 848

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 849

This theorem is referenced by:  pm4.25  906  orordi  929  orordir  930  nornot  1533  truortru  1579  falorfal  1582  unidm  4111  dfsn2ALT  4604  preqsnd  4817  tz7.48lem  8382  msq0i  11798  msq0d  11799  prmdvdsexp  16654  metn0  24316  rrxcph  25360  nb3grprlem2  29466  pm11.7  44752  euoreqb  47469