Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e1bir Unicode version

Theorem e1bir 28402
Description: Right biconditional form of e1_ 28399. sylibr 203 is e1bir 28402 without virtual deductions. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e1bir.1  |-  (. ph  ->.  ps
).
e1bir.2  |-  ( ch  <->  ps )
Assertion
Ref Expression
e1bir  |-  (. ph  ->.  ch
).

Proof of Theorem e1bir
StepHypRef Expression
1 e1bir.1 . 2  |-  (. ph  ->.  ps
).
2 e1bir.2 . . 3  |-  ( ch  <->  ps )
32biimpri 197 . 2  |-  ( ps 
->  ch )
41, 3e1_ 28399 1  |-  (. ph  ->.  ch
).
Colors of variables: wff set class
Syntax hints:    <-> wb 176   (.wvd1 28337
This theorem is referenced by:  en3lplem2VD  28620
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-vd1 28338
  Copyright terms: Public domain W3C validator