Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sbaniota Unicode version

Theorem sbaniota 27046
Description: Theorem *14.26 in [WhiteheadRussell] p. 192. (Contributed by Andrew Salmon, 12-Jul-2011.)
Assertion
Ref Expression
sbaniota  |-  ( E! x ph  ->  ( E. x ( ph  /\  ps )  <->  [. ( iota x ph )  /  x ]. ps ) )

Proof of Theorem sbaniota
StepHypRef Expression
1 eupickbi 2210 . 2  |-  ( E! x ph  ->  ( E. x ( ph  /\  ps )  <->  A. x ( ph  ->  ps ) ) )
2 sbiota1 27045 . 2  |-  ( E! x ph  ->  ( A. x ( ph  ->  ps )  <->  [. ( iota x ph )  /  x ]. ps ) )
31, 2bitrd 244 1  |-  ( E! x ph  ->  ( E. x ( ph  /\  ps )  <->  [. ( iota x ph )  /  x ]. ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358   A.wal 1527   E.wex 1528   E!weu 2144   [.wsbc 2992   iotacio 6251
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868  ax-ext 2265
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1631  df-eu 2148  df-mo 2149  df-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-ral 2549  df-rex 2550  df-v 2791  df-sbc 2993  df-un 3158  df-sn 3647  df-pr 3648  df-uni 3829  df-iota 6253
  Copyright terms: Public domain W3C validator