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Theorem e3 28512
Description: Meta-connective form of syl8 65. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e3.1  |-  (. ph ,. ps ,. ch  ->.  th ).
e3.2  |-  ( th 
->  ta )
Assertion
Ref Expression
e3  |-  (. ph ,. ps ,. ch  ->.  ta ).

Proof of Theorem e3
StepHypRef Expression
1 e3.1 . 2  |-  (. ph ,. ps ,. ch  ->.  th ).
2 e3.2 . . 3  |-  ( th 
->  ta )
32a1i 10 . 2  |-  ( th 
->  ( th  ->  ta ) )
41, 1, 3e33 28509 1  |-  (. ph ,. ps ,. ch  ->.  ta ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd3 28356
This theorem is referenced by:  e3bi  28513  e3bir  28514  truniALTVD  28654  onfrALTlem2VD  28665
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 28359
  Copyright terms: Public domain W3C validator