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Theorem dfvd3an 28686
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 28661 . 2  |-  ( (.
(. ph ,. ps ,. ch ).  ->.  th ).  <->  ( (. ph ,. ps ,. ch ).  ->  th ) )
2 df-vhc3 28681 . . 3  |-  ( (.
ph ,. ps ,. ch ).  <->  ( ph  /\  ps  /\  ch ) )
32imbi1i 316 . 2  |-  ( ( (. ph ,. ps ,. ch ).  ->  th )  <->  ( ( ph  /\  ps  /\ 
ch )  ->  th )
)
41, 3bitri 241 1  |-  ( (.
(. ph ,. ps ,. ch ).  ->.  th ).  <->  ( ( ph  /\  ps  /\  ch )  ->  th ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ w3a 936   (.wvd1 28660   (.wvhc3 28680
This theorem is referenced by:  dfvd3ani  28687  dfvd3anir  28688
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 178  df-vd1 28661  df-vhc3 28681
  Copyright terms: Public domain W3C validator