Theorem oridm 918

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		pm1.2 917	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 916	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 212	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

This proof depends on syntax axioms:   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  pm4.25  919  orordi  942  orordir  943  nornot  1561  truortru  1607  falorfal  1610  unidm  4111  dfsn2ALT  4613  preqsnd  4826  tz7.48lem  8434  msq0i  11878  msq0d  11879  prmdvdsexp  16796  metn0  24568  rrxcph  25602  nb3grprlem2  29789  pm11.7  45164  euoreqb  47904