Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj832 Unicode version

Theorem bnj832 28787
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj832.1  |-  ( et  <->  (
ph  /\  ps )
)
bnj832.2  |-  ( ph  ->  ta )
Assertion
Ref Expression
bnj832  |-  ( et 
->  ta )

Proof of Theorem bnj832
StepHypRef Expression
1 bnj832.1 . 2  |-  ( et  <->  (
ph  /\  ps )
)
2 bnj832.2 . . 3  |-  ( ph  ->  ta )
32adantr 451 . 2  |-  ( (
ph  /\  ps )  ->  ta )
41, 3sylbi 187 1  |-  ( et 
->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  bnj1379  28863  bnj605  28939  bnj908  28963  bnj1145  29023  bnj1442  29079  bnj1450  29080  bnj1489  29086  bnj1501  29097  bnj1523  29101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator