Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj248 Structured version   Unicode version

Theorem bnj248 32850
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj248  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( (
( ph  /\  ps )  /\  ch )  /\  th ) )

Proof of Theorem bnj248
StepHypRef Expression
1 df-bnj17 32837 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( ( ph  /\  ps  /\  ch )  /\  th ) )
2 df-3an 975 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
32anbi1i 695 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th ) 
<->  ( ( ( ph  /\ 
ps )  /\  ch )  /\  th ) )
41, 3bitri 249 1  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  <->  ( (
( ph  /\  ps )  /\  ch )  /\  th ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    /\ w3a 973    /\ w-bnj17 32836
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 185  df-an 371  df-3an 975  df-bnj17 32837
This theorem is referenced by:  bnj253  32854  bnj256  32856  bnj605  33062  bnj908  33086
  Copyright terms: Public domain W3C validator