Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e2bir Unicode version

Theorem e2bir 28077
Description: Right bi-conditional form of e2 28075. syl6ibr 219 is e2bir 28077 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 198 . 2  |-  ( ch 
->  th )
41, 3e2 28075 1  |-  (. ph ,. ps  ->.  th ).
Colors of variables: wff set class
Syntax hints:    <-> wb 177   (.wvd2 28012
This theorem is referenced by:  trsspwALT  28274  pwtrVD  28280  eqsbc3rVD  28295  tpid3gVD  28297  onfrALTlem1VD  28345
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 178  df-an 361  df-vd2 28013
  Copyright terms: Public domain W3C validator