Theorem oridm 765

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		pm1.2 764	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 745	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 126	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 105   ∨ wo 716

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm4.25  766  orordi  781  orordir  782  truortru  1450  falorfal  1453  truxortru  1464  falxorfal  1467  unidm  3362  preqsn  3879  funopsn  5860  reapirr  8851  reapti  8853  lt2msq  9160  nn0ge2m1nn  9560  absext  11748  prmdvdsexp  12845  sqpweven  12872  2sqpwodd  12873