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

Theorem bnj832 32105
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 465 . 2  |-  ( (
ph  /\  ps )  ->  ta )
41, 3sylbi 195 1  |-  ( et 
->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369
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
This theorem is referenced by:  bnj1379  32179  bnj605  32255  bnj908  32279  bnj1145  32339  bnj1442  32395  bnj1450  32396  bnj1489  32402  bnj1501  32413  bnj1523  32417
  Copyright terms: Public domain W3C validator