Theorem oridm 762

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		pm1.2 761	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 742	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 126	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 105   ∨ wo 713

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 714

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm4.25  763  orordi  778  orordir  779  truortru  1447  falorfal  1450  truxortru  1461  falxorfal  1464  unidm  3347  preqsn  3852  funopsn  5816  reapirr  8720  reapti  8722  lt2msq  9029  nn0ge2m1nn  9425  absext  11569  prmdvdsexp  12665  sqpweven  12692  2sqpwodd  12693