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  3352  preqsn  3863  funopsn  5838  reapirr  8799  reapti  8801  lt2msq  9108  nn0ge2m1nn  9506  absext  11686  prmdvdsexp  12783  sqpweven  12810  2sqpwodd  12811