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Theorem dfvd3ani 33785
Description: Inference form of dfvd3an 33784. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd3ani.1  |-  (. (. ph ,. ps ,. ch ).  ->.  th ).
Assertion
Ref Expression
dfvd3ani  |-  ( (
ph  /\  ps  /\  ch )  ->  th )

Proof of Theorem dfvd3ani
StepHypRef Expression
1 dfvd3ani.1 . 2  |-  (. (. ph ,. ps ,. ch ).  ->.  th ).
2 dfvd3an 33784 . 2  |-  ( (.
(. ph ,. ps ,. ch ).  ->.  th ).  <->  ( ( ph  /\  ps  /\  ch )  ->  th ) )
31, 2mpbi 208 1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 971   (.wvd1 33759   (.wvhc3 33778
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-vhc3 33779
This theorem is referenced by:  int3  33811  el0321old  33925
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