Theorem oridm 764

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		pm1.2 763	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 744	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 126	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 105   ∨ wo 715

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 716

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm4.25  765  orordi  780  orordir  781  truortru  1449  falorfal  1452  truxortru  1463  falxorfal  1466  unidm  3350  preqsn  3858  funopsn  5829  reapirr  8756  reapti  8758  lt2msq  9065  nn0ge2m1nn  9461  absext  11623  prmdvdsexp  12719  sqpweven  12746  2sqpwodd  12747