Theorem oridm 715

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		pm1.2 714	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 697	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 125	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 104   ∨ wo 670

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm4.25  716  orordi  731  orordir  732  truortru  1351  falorfal  1354  truxortru  1365  falxorfal  1368  unidm  3166  preqsn  3649  reapirr  8205  reapti  8207  lt2msq  8502  nn0ge2m1nn  8889  absext  10675  prmdvdsexp  11619  sqpweven  11645  2sqpwodd  11646