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 31077
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 31073 . 2 ((𝜑𝜓𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
2 df-3an 1074 . 2 (((𝜑𝜓) ∧ 𝜒𝜃) ↔ (((𝜑𝜓) ∧ 𝜒) ∧ 𝜃))
31, 2bitr4i 267 1 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓) ∧ 𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 383  w3a 1072  w-bnj17 31059
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 31060
This theorem is referenced by:  bnj543  31268  bnj558  31277  bnj594  31287  bnj917  31309  bnj929  31311  bnj944  31313  bnj978  31324  bnj998  31331  bnj1006  31334
  Copyright terms: Public domain W3C validator