MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  an43 Structured version   Visualization version   GIF version

Theorem an43 863
Description: Rearrangement of 4 conjuncts. (Contributed by Rodolfo Medina, 24-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
an43 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜃) ∧ (𝜓𝜒)))

Proof of Theorem an43
StepHypRef Expression
1 an42 862 . 2 (((𝜑𝜃) ∧ (𝜓𝜒)) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
21bicomi 213 1 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜃) ∧ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 195  wa 383
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 196  df-an 385
This theorem is referenced by:  an3  864  prtlem15  33178
  Copyright terms: Public domain W3C validator