Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfvd2an Structured version   Unicode version

Theorem dfvd2an 36396
Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dfvd2an  |-  ( (.
(. ph ,. ps ).  ->.  ch
). 
<->  ( ( ph  /\  ps )  ->  ch )
)

Proof of Theorem dfvd2an
StepHypRef Expression
1 df-vd1 36384 . 2  |-  ( (.
(. ph ,. ps ).  ->.  ch
). 
<->  ( (. ph ,. ps ).  ->  ch )
)
2 df-vhc2 36395 . . 3  |-  ( (.
ph ,. ps ).  <->  (
ph  /\  ps )
)
32imbi1i 325 . 2  |-  ( ( (. ph ,. ps ).  ->  ch )  <->  ( ( ph  /\  ps )  ->  ch ) )
41, 3bitri 251 1  |-  ( (.
(. ph ,. ps ).  ->.  ch
). 
<->  ( ( ph  /\  ps )  ->  ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 186    /\ wa 369   (.wvd1 36383   (.wvhc2 36394
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 187  df-vd1 36384  df-vhc2 36395
This theorem is referenced by:  dfvd2ani  36397  dfvd2anir  36398  iden2  36437
  Copyright terms: Public domain W3C validator