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Theorem pm14.18 27028
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 27018 . 2  |-  ( E! x ph  ->  ( iota x ph )  e. 
_V )
2 spsbc 3005 . 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 1528    e. wcel 1685   E!weu 2145   _Vcvv 2790   [.wsbc 2993   iotacio 6251
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868  ax-ext 2266
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1312  df-ex 1530  df-nf 1533  df-sb 1632  df-eu 2149  df-clab 2272  df-cleq 2278  df-clel 2281  df-nfc 2410  df-rex 2551  df-v 2792  df-sbc 2994  df-un 3159  df-sn 3648  df-pr 3649  df-uni 3830  df-iota 6253
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