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Theorem dfvd2anir 33774
Description: Right-to-left inference form of dfvd2an 33772. (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 33772 . 2  |-  ( (.
(. ph ,. ps ).  ->.  ch
). 
<->  ( ( ph  /\  ps )  ->  ch )
)
31, 2mpbir 209 1  |-  (. (. ph ,. ps ).  ->.  ch ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367   (.wvd1 33759   (.wvhc2 33770
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-vd1 33760  df-vhc2 33771
This theorem is referenced by:  int3  33811  el021old  33900  el2122old  33927  el12  33936
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