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Theorem dfvd2an 28675
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 28662 . 2  |-  ( (.
(. ph ,. ps ).  ->.  ch
). 
<->  ( (. ph ,. ps ).  ->  ch )
)
2 df-vhc2 28674 . . 3  |-  ( (.
ph ,. ps ).  <->  (
ph  /\  ps )
)
32imbi1i 317 . 2  |-  ( ( (. ph ,. ps ).  ->  ch )  <->  ( ( ph  /\  ps )  ->  ch ) )
41, 3bitri 242 1  |-  ( (.
(. ph ,. ps ).  ->.  ch
). 
<->  ( ( ph  /\  ps )  ->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    /\ wa 360   (.wvd1 28661   (.wvhc2 28673
This theorem is referenced by:  dfvd2ani  28676  dfvd2anir  28677  iden2  28716
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 179  df-vd1 28662  df-vhc2 28674
  Copyright terms: Public domain W3C validator