Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj268 Structured version   Visualization version   GIF version

Theorem bnj268 30749
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj268 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜓𝜃))

Proof of Theorem bnj268
StepHypRef Expression
1 3ancomb 1045 . . 3 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
21anbi1i 730 . 2 (((𝜑𝜓𝜒) ∧ 𝜃) ↔ ((𝜑𝜒𝜓) ∧ 𝜃))
3 df-bnj17 30727 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
4 df-bnj17 30727 . 2 ((𝜑𝜒𝜓𝜃) ↔ ((𝜑𝜒𝜓) ∧ 𝜃))
52, 3, 43bitr4i 292 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜒𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 384  w3a 1036  w-bnj17 30726
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 197  df-an 386  df-3an 1038  df-bnj17 30727
This theorem is referenced by:  bnj543  30937  bnj929  30980  bnj1110  31024
  Copyright terms: Public domain W3C validator