Theorem oridm 757

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		pm1.2 756	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 737	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 126	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 105   ∨ wo 708

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 709

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm4.25  758  orordi  773  orordir  774  truortru  1405  falorfal  1408  truxortru  1419  falxorfal  1422  unidm  3278  preqsn  3775  reapirr  8532  reapti  8534  lt2msq  8841  nn0ge2m1nn  9234  absext  11067  prmdvdsexp  12142  sqpweven  12169  2sqpwodd  12170