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Theorem e33 28823
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e33.1  |-  (. ph ,. ps ,. ch  ->.  th ).
e33.2  |-  (. ph ,. ps ,. ch  ->.  ta ).
e33.3  |-  ( th 
->  ( ta  ->  et ) )
Assertion
Ref Expression
e33  |-  (. ph ,. ps ,. ch  ->.  et ).

Proof of Theorem e33
StepHypRef Expression
1 e33.1 . 2  |-  (. ph ,. ps ,. ch  ->.  th ).
2 e33.2 . 2  |-  (. ph ,. ps ,. ch  ->.  ta ).
3 e33.3 . . 3  |-  ( th 
->  ( ta  ->  et ) )
43a1i 10 . 2  |-  ( th 
->  ( th  ->  ( ta  ->  et ) ) )
51, 1, 2, 4e333 28822 1  |-  (. ph ,. ps ,. ch  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd3 28655
This theorem is referenced by:  e33an  28824  e3  28826  e03  28829  e30  28833  e13  28837  e31  28840  e23  28844  e32  28847  truniALTVD  28970  trintALTVD  28972  onfrALTlem2VD  28981
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-an 360  df-3an 936  df-vd3 28658
  Copyright terms: Public domain W3C validator