Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj645 Structured version   Visualization version   GIF version

Theorem bnj645 31289
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj645 ((𝜑𝜓𝜒𝜃) → 𝜃)

Proof of Theorem bnj645
StepHypRef Expression
1 df-bnj17 31225 . 2 ((𝜑𝜓𝜒𝜃) ↔ ((𝜑𝜓𝜒) ∧ 𝜃))
21simprbi 490 1 ((𝜑𝜓𝜒𝜃) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1107  w-bnj17 31224
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-bnj17 31225
This theorem is referenced by:  bnj708  31295  bnj908  31470  bnj929  31475  bnj964  31482  bnj1110  31519
  Copyright terms: Public domain W3C validator