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Theorem dfvd2anir 28678
Description: Right-to-left inference form of dfvd2an 28676. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd2anir.1  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
dfvd2anir  |-  (. (. ph ,. ps ).  ->.  ch ).

Proof of Theorem dfvd2anir
StepHypRef Expression
1 dfvd2anir.1 . 2  |-  ( (
ph  /\  ps )  ->  ch )
2 dfvd2an 28676 . 2  |-  ( (.
(. ph ,. ps ).  ->.  ch
). 
<->  ( ( ph  /\  ps )  ->  ch )
)
31, 2mpbir 202 1  |-  (. (. ph ,. ps ).  ->.  ch ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360   (.wvd1 28662   (.wvhc2 28674
This theorem is referenced by:  int3  28715  el021old  28804  el2122old  28831  el12  28840
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 28663  df-vhc2 28675
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