Theorem oridm 769

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		pm1.2 768	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 749	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 126	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 105   ∨ wo 720

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 721

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm4.25  770  orordi  785  orordir  786  truortru  1454  falorfal  1457  truxortru  1468  falxorfal  1471  unidm  3372  preqsn  3895  funopsn  5882  reapirr  8895  reapti  8897  lt2msq  9206  nn0ge2m1nn  9606  absext  11807  prmdvdsexp  12904  sqpweven  12931  2sqpwodd  12932