Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj771 Structured version   Unicode version

Theorem bnj771 29363
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj771.1  |-  ( et  <->  (
ph  /\  ps  /\  ch  /\ 
th ) )
bnj771.2  |-  ( ch 
->  ta )
Assertion
Ref Expression
bnj771  |-  ( et 
->  ta )

Proof of Theorem bnj771
StepHypRef Expression
1 bnj771.1 . 2  |-  ( et  <->  (
ph  /\  ps  /\  ch  /\ 
th ) )
2 bnj771.2 . . 3  |-  ( ch 
->  ta )
32bnj707 29353 . 2  |-  ( (
ph  /\  ps  /\  ch  /\ 
th )  ->  ta )
41, 3sylbi 198 1  |-  ( et 
->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187    /\ w-bnj17 29279
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 188  df-an 372  df-3an 984  df-bnj17 29280
This theorem is referenced by:  bnj1247  29408  bnj996  29554  bnj1097  29578  bnj1145  29590  bnj1259  29613  bnj1296  29618  bnj1450  29647
  Copyright terms: Public domain W3C validator