Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfvd3an Structured version   Visualization version   Unicode version

Theorem dfvd3an 37032
Description: Definition of a 3-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dfvd3an  |-  ( (.
(. ph ,. ps ,. ch ).  ->.  th ).  <->  ( ( ph  /\  ps  /\  ch )  ->  th ) )

Proof of Theorem dfvd3an
StepHypRef Expression
1 df-vd1 37008 . 2  |-  ( (.
(. ph ,. ps ,. ch ).  ->.  th ).  <->  ( (. ph ,. ps ,. ch ).  ->  th ) )
2 df-vhc3 37027 . . 3  |-  ( (.
ph ,. ps ,. ch ).  <->  ( ph  /\  ps  /\  ch ) )
32imbi1i 332 . 2  |-  ( ( (. ph ,. ps ,. ch ).  ->  th )  <->  ( ( ph  /\  ps  /\ 
ch )  ->  th )
)
41, 3bitri 257 1  |-  ( (.
(. ph ,. ps ,. ch ).  ->.  th ).  <->  ( ( ph  /\  ps  /\  ch )  ->  th ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189    /\ w3a 1007   (.wvd1 37007   (.wvhc3 37026
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 190  df-vd1 37008  df-vhc3 37027
This theorem is referenced by:  dfvd3ani  37033  dfvd3anir  37034
  Copyright terms: Public domain W3C validator