Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfvd3 Unicode version

Theorem dfvd3 28659
Description: Definition of a 3-hypothesis virtual deduction. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dfvd3  |-  ( (.
ph ,. ps ,. ch  ->.  th ).  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )

Proof of Theorem dfvd3
StepHypRef Expression
1 df-vd3 28658 . 2  |-  ( (.
ph ,. ps ,. ch  ->.  th ).  <->  ( ( ph  /\  ps  /\  ch )  ->  th ) )
2 df-3an 936 . . . . 5  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
32imbi1i 315 . . . 4  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  th )  <->  ( ( ( ph  /\  ps )  /\  ch )  ->  th ) )
4 impexp 433 . . . 4  |-  ( ( ( ( ph  /\  ps )  /\  ch )  ->  th )  <->  ( ( ph  /\  ps )  -> 
( ch  ->  th )
) )
53, 4bitri 240 . . 3  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  th )  <->  ( ( ph  /\  ps )  ->  ( ch  ->  th ) ) )
6 impexp 433 . . 3  |-  ( ( ( ph  /\  ps )  ->  ( ch  ->  th ) )  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
75, 6bitri 240 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  ->  th )  <->  (
ph  ->  ( ps  ->  ( ch  ->  th )
) ) )
81, 7bitri 240 1  |-  ( (.
ph ,. ps ,. ch  ->.  th ).  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358    /\ w3a 934   (.wvd3 28655
This theorem is referenced by:  dfvd3i  28660  dfvd3ir  28661
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  df-3an 936  df-vd3 28658
  Copyright terms: Public domain W3C validator