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Theorem e2bi 33561
Description: Biconditional form of e2 33560. syl6ib 226 is e2bi 33561 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 194 . 2  |-  ( ch 
->  th )
41, 3e2 33560 1  |-  (. ph ,. ps  ->.  th ).
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   (.wvd2 33497
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 33498
This theorem is referenced by:  snssiALTVD  33770  eqsbc3rVD  33783  en3lplem2VD  33787  onfrALTlem3VD  33830  onfrALTlem1VD  33833
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