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  1531  truortru  1577  falorfal  1580  unidm  4116  dfsn2ALT  4607  preqsnd  4819  sucexeloniOLD  7766  tz7.48lem  8386  msq0i  11803  msq0d  11804  prmdvdsexp  16661  metn0  24224  rrxcph  25268  nb3grprlem2  29284  pm11.7  44358  euoreqb  47083