Theorem oridm 904

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		pm1.2 903	. 2 ⊢ ((𝜑 ∨ 𝜑) → 𝜑)
2		pm2.07 902	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜑))
3	1, 2	impbii 209	1 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)

Syntax hints:   ↔ wb 206   ∨ wo 847

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-or 848

This theorem is referenced by:  pm4.25  905  orordi  928  orordir  929  nornot  1531  truortru  1577  falorfal  1580  unidm  4108  dfsn2ALT  4599  preqsnd  4810  tz7.48lem  8363  msq0i  11769  msq0d  11770  prmdvdsexp  16626  metn0  24246  rrxcph  25290  nb3grprlem2  29326  pm11.7  44369  euoreqb  47093