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Theorem e2bi 28404
Description: Bi-conditional form of e2 28403. syl6ib 217 is e2bi 28404 without virtual deductions. (Contributed by Alan Sare, 10-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e2bi.1  |-  (. ph ,. ps  ->.  ch ).
e2bi.2  |-  ( ch  <->  th )
Assertion
Ref Expression
e2bi  |-  (. ph ,. ps  ->.  th ).

Proof of Theorem e2bi
StepHypRef Expression
1 e2bi.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e2bi.2 . . 3  |-  ( ch  <->  th )
32biimpi 186 . 2  |-  ( ch 
->  th )
41, 3e2 28403 1  |-  (. ph ,. ps  ->.  th ).
Colors of variables: wff set class
Syntax hints:    <-> wb 176   (.wvd2 28346
This theorem is referenced by:  snssiALTVD  28602  eqsbc3rVD  28616  en3lplem2VD  28620  onfrALTlem3VD  28663  onfrALTlem1VD  28666
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 28347
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