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Theorem pm14.18 36773
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 36763 . 2  |-  ( E! x ph  ->  ( iota x ph )  e. 
_V )
2 spsbc 3279 . 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 setvar class
Syntax hints:    -> wi 4   A.wal 1441    e. wcel 1886   E!weu 2298   _Vcvv 3044   [.wsbc 3266   iotacio 5543
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-eu 2302  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-rex 2742  df-v 3046  df-sbc 3267  df-un 3408  df-sn 3968  df-pr 3970  df-uni 4198  df-iota 5545
This theorem is referenced by: (None)
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