Theorem oridm 918

Description: Idempotent law for disjunction. Theorem *4.25 of [WhiteheadRussell] p. 117. (Contributed by NM, 11-May-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		pm1.2 917	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 916	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 212	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

This proof depends on syntax axioms:   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  pm4.25  919  orordi  942  orordir  943  nornot  1561  truortru  1607  falorfal  1610  unidm  4159  dfsn2ALT  4606  preqsnd  4819  tz7.48lemOLD  8489  msq0i  12005  msq0d  12006  prmdvdsexp  16935  metn0  24734  rrxcph  25768  nb3grprlem2  30019  pm11.7  45641  euoreqb  48453