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Theorem dfvd2imp 28375
Description: The virtual deduction form of a 2-antecedent nested implication implies the 2-antecedent nested implication. (Contributed by Alan Sare, 21-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dfvd2imp  |-  ( (.
ph ,. ps  ->.  ch ).  ->  (
ph  ->  ( ps  ->  ch ) ) )

Proof of Theorem dfvd2imp
StepHypRef Expression
1 dfvd2 28348 . 2  |-  ( (.
ph ,. ps  ->.  ch ).  <->  ( ph  ->  ( ps  ->  ch ) ) )
21biimpi 186 1  |-  ( (.
ph ,. ps  ->.  ch ).  ->  (
ph  ->  ( ps  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd2 28346
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-vd2 28347
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