Theorem oridm 758

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		pm1.2 757	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 738	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 126	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 105   ∨ wo 709

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 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm4.25  759  orordi  774  orordir  775  truortru  1416  falorfal  1419  truxortru  1430  falxorfal  1433  unidm  3293  preqsn  3790  reapirr  8565  reapti  8567  lt2msq  8874  nn0ge2m1nn  9267  absext  11107  prmdvdsexp  12183  sqpweven  12210  2sqpwodd  12211