Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj257 Structured version   Visualization version   GIF version

Theorem bnj257 31103
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj257 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓𝜃𝜒))

Proof of Theorem bnj257
StepHypRef Expression
1 ancom 465 . . 3 ((𝜒𝜃) ↔ (𝜃𝜒))
21anbi2i 732 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) ↔ ((𝜑𝜓) ∧ (𝜃𝜒)))
3 bnj256 31102 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ (𝜒𝜃)))
4 bnj256 31102 . 2 ((𝜑𝜓𝜃𝜒) ↔ ((𝜑𝜓) ∧ (𝜃𝜒)))
52, 3, 43bitr4i 292 1 ((𝜑𝜓𝜒𝜃) ↔ (𝜑𝜓𝜃𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 383  w-bnj17 31082
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 385  df-3an 1074  df-bnj17 31083
This theorem is referenced by:  bnj258  31104  bnj334  31109  bnj543  31291  bnj929  31334
  Copyright terms: Public domain W3C validator