Theorem oridm 759

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		pm1.2 758	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 739	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 126	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 105   ∨ wo 710

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 711

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm4.25  760  orordi  775  orordir  776  truortru  1425  falorfal  1428  truxortru  1439  falxorfal  1442  unidm  3320  preqsn  3822  funopsn  5775  reapirr  8670  reapti  8672  lt2msq  8979  nn0ge2m1nn  9375  absext  11449  prmdvdsexp  12545  sqpweven  12572  2sqpwodd  12573