Users' Mathboxes Mathbox for Andrew Salmon < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pm14.18 Unicode version

Theorem pm14.18 26982
Description: Theorem *14.18 in [WhiteheadRussell] p. 189. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
pm14.18  |-  ( E! x ph  ->  ( A. x ps  ->  [. ( iota x ph )  /  x ]. ps ) )

Proof of Theorem pm14.18
StepHypRef Expression
1 iotaexeu 26972 . 2  |-  ( E! x ph  ->  ( iota x ph )  e. 
_V )
2 a4sbc 2964 . 2  |-  ( ( iota x ph )  e.  _V  ->  ( A. x ps  ->  [. ( iota x ph )  /  x ]. ps ) )
31, 2syl 17 1  |-  ( E! x ph  ->  ( A. x ps  ->  [. ( iota x ph )  /  x ]. ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532    e. wcel 1621   E!weu 2117   _Vcvv 2757   [.wsbc 2952   iotacio 6209
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2121  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-rex 2522  df-v 2759  df-sbc 2953  df-un 3118  df-sn 3606  df-pr 3607  df-uni 3788  df-iota 6211
  Copyright terms: Public domain W3C validator