Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfvd3anir Unicode version

Theorem dfvd3anir 28365
Description: Right-to-left inference form of dfvd3an 28363. (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 28363 . 2  |-  ( (.
(. ph ,. ps ,. ch ).  ->.  th ).  <->  ( ( ph  /\  ps  /\  ch )  ->  th ) )
31, 2mpbir 200 1  |-  (. (. ph ,. ps ,. ch ).  ->.  th ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934   (.wvd1 28337   (.wvhc3 28357
This theorem is referenced by:  el0321old  28496  el123  28539
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 177  df-vd1 28338  df-vhc3 28358
  Copyright terms: Public domain W3C validator