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  3853  funopsn  5819  reapirr  8735  reapti  8737  lt2msq  9044  nn0ge2m1nn  9440  absext  11589  prmdvdsexp  12685  sqpweven  12712  2sqpwodd  12713