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Theorem dfvd3anir 36966
Description: Right-to-left inference form of dfvd3an 36964. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd3anir.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
dfvd3anir  |-  (. (. ph ,. ps ,. ch ).  ->.  th ).

Proof of Theorem dfvd3anir
StepHypRef Expression
1 dfvd3anir.1 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
2 dfvd3an 36964 . 2  |-  ( (.
(. ph ,. ps ,. ch ).  ->.  th ).  <->  ( ( ph  /\  ps  /\  ch )  ->  th ) )
31, 2mpbir 213 1  |-  (. (. ph ,. ps ,. ch ).  ->.  th ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 985   (.wvd1 36939   (.wvhc3 36958
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 189  df-vd1 36940  df-vhc3 36959
This theorem is referenced by:  el0321old  37102  el123  37151
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