Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj253 Structured version   Visualization version   GIF version

Theorem bnj253 34697
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj253 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ 𝜒𝜃))

Proof of Theorem bnj253
StepHypRef Expression
1 bnj248 34693 . 2 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
2 df-3an 1088 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
31, 2bitr4i 278 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ 𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 206  wa 395  w3a 1086  w-bnj17 34679
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 207  df-an 396  df-3an 1088  df-bnj17 34680
This theorem is referenced by:  bnj543  34886  bnj558  34895  bnj594  34905  bnj917  34927  bnj929  34929  bnj944  34931  bnj978  34942  bnj998  34950  bnj1006  34953
  Copyright terms: Public domain W3C validator