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Theorem dfvd3ir 28403
Description: Right-to-left inference form of dfvd3 28401. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd3ir.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
dfvd3ir  |-  (. ph ,. ps ,. ch  ->.  th ).

Proof of Theorem dfvd3ir
StepHypRef Expression
1 dfvd3ir.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 dfvd3 28401 . 2  |-  ( (.
ph ,. ps ,. ch  ->.  th ).  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
31, 2mpbir 201 1  |-  (. ph ,. ps ,. ch  ->.  th ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd3 28397
This theorem is referenced by:  vd03  28418  vd13  28420  vd23  28421  in3an  28430  idn3  28434  gen31  28440  e223  28454  e333  28563  e233  28595  e323  28596
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-an 361  df-3an 938  df-vd3 28400
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