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Theorem e2bir 31652
Description: Right bi-conditional form of e2 31650. syl6ibr 227 is e2bir 31652 without virtual deductions. (Contributed by Alan Sare, 29-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e2bir.1  |-  (. ph ,. ps  ->.  ch ).
e2bir.2  |-  ( th  <->  ch )
Assertion
Ref Expression
e2bir  |-  (. ph ,. ps  ->.  th ).

Proof of Theorem e2bir
StepHypRef Expression
1 e2bir.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e2bir.2 . . 3  |-  ( th  <->  ch )
32biimpri 206 . 2  |-  ( ch 
->  th )
41, 3e2 31650 1  |-  (. ph ,. ps  ->.  th ).
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   (.wvd2 31587
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-an 371  df-vd2 31588
This theorem is referenced by:  trsspwALT  31849  pwtrVD  31857  eqsbc3rVD  31873  tpid3gVD  31875  onfrALTlem1VD  31923
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