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Theorem e2bir 28710
Description: Right bi-conditional form of e2 28708. syl6ibr 218 is e2bir 28710 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 197 . 2  |-  ( ch 
->  th )
41, 3e2 28708 1  |-  (. ph ,. ps  ->.  th ).
Colors of variables: wff set class
Syntax hints:    <-> wb 176   (.wvd2 28645
This theorem is referenced by:  trsspwALT  28908  pwtrVD  28914  eqsbc3rVD  28932  tpid3gVD  28934  onfrALTlem1VD  28982
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-vd2 28646
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