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Theorem e2bi 37011
Description: Biconditional form of e2 37010. syl6ib 230 is e2bi 37011 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 198 . 2  |-  ( ch 
->  th )
41, 3e2 37010 1  |-  (. ph ,. ps  ->.  th ).
Colors of variables: wff setvar class
Syntax hints:    <-> wb 188   (.wvd2 36947
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 189  df-an 373  df-vd2 36948
This theorem is referenced by:  snssiALTVD  37223  eqsbc3rVD  37236  en3lplem2VD  37240  onfrALTlem3VD  37284  onfrALTlem1VD  37287
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