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Theorem dfvd3anir 28688
Description: Right-to-left inference form of dfvd3an 28686. (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 28686 . 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    /\ w3a 936   (.wvd1 28660   (.wvhc3 28680
This theorem is referenced by:  el0321old  28827  el123  28876
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-vd1 28661  df-vhc3 28681
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