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Theorem dfvd2 33499
Description: Definition of a 2-hypothesis virtual deduction. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dfvd2  |-  ( (.
ph ,. ps  ->.  ch ).  <->  ( ph  ->  ( ps  ->  ch ) ) )

Proof of Theorem dfvd2
StepHypRef Expression
1 df-vd2 33498 . 2  |-  ( (.
ph ,. ps  ->.  ch ).  <->  ( ( ph  /\  ps )  ->  ch ) )
2 impexp 446 . 2  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ph  ->  ( ps  ->  ch ) ) )
31, 2bitri 249 1  |-  ( (.
ph ,. ps  ->.  ch ).  <->  ( ph  ->  ( ps  ->  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369   (.wvd2 33497
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 185  df-an 371  df-vd2 33498
This theorem is referenced by:  dfvd2i  33505  dfvd2ir  33506  dfvd2imp  33532  dfvd2impr  33533
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