Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj291 Structured version   Visualization version   GIF version

Theorem bnj291 31228
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj291 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜒𝜃) ∧ 𝜓))

Proof of Theorem bnj291
StepHypRef Expression
1 bnj290 31227 . 2 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜃𝜓))
2 df-bnj17 31204 . 2 ((𝜑𝜒𝜃𝜓) ↔ ((𝜑𝜒𝜃) ∧ 𝜓))
31, 2bitri 266 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜒𝜃) ∧ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 197  wa 384  w3a 1107  w-bnj17 31203
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 198  df-an 385  df-3an 1109  df-bnj17 31204
This theorem is referenced by:  bnj643  31267  bnj938  31455  bnj944  31456
  Copyright terms: Public domain W3C validator