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Theorem pm14.18 27543
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 27533 . 2  |-  ( E! x ph  ->  ( iota x ph )  e. 
_V )
2 spsbc 3165 . 2  |-  ( ( iota x ph )  e.  _V  ->  ( A. x ps  ->  [. ( iota x ph )  /  x ]. ps ) )
31, 2syl 16 1  |-  ( E! x ph  ->  ( A. x ps  ->  [. ( iota x ph )  /  x ]. ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549    e. wcel 1725   E!weu 2280   _Vcvv 2948   [.wsbc 3153   iotacio 5407
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-v 2950  df-sbc 3154  df-un 3317  df-sn 3812  df-pr 3813  df-uni 4008  df-iota 5409
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