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Theorem e3bi 28827
Description: Biconditional form of e3 28826. syl8ib 222 is e3bi 28827 without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e3bi.1  |-  (. ph ,. ps ,. ch  ->.  th ).
e3bi.2  |-  ( th  <->  ta )
Assertion
Ref Expression
e3bi  |-  (. ph ,. ps ,. ch  ->.  ta ).

Proof of Theorem e3bi
StepHypRef Expression
1 e3bi.1 . 2  |-  (. ph ,. ps ,. ch  ->.  th ).
2 e3bi.2 . . 3  |-  ( th  <->  ta )
32biimpi 186 . 2  |-  ( th 
->  ta )
41, 3e3 28826 1  |-  (. ph ,. ps ,. ch  ->.  ta ).
Colors of variables: wff set class
Syntax hints:    <-> wb 176   (.wvd3 28655
This theorem is referenced by:  en3lplem2VD  28936
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