MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  orabs Structured version   Visualization version   GIF version

Theorem orabs 992
Description: Absorption of redundant internal disjunct. Compare Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Wolf Lammen, 28-Feb-2014.)
Assertion
Ref Expression
orabs (𝜑 ↔ ((𝜑𝜓) ∧ 𝜑))

Proof of Theorem orabs
StepHypRef Expression
1 orc 861 . 2 (𝜑 → (𝜑𝜓))
21pm4.71ri 561 1 (𝜑 ↔ ((𝜑𝜓) ∧ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  wo 841
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 208  df-an 397  df-or 842
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator