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Theorem iotasbcq 27036
Description: Theorem *14.272 in [WhiteheadRussell] p. 193. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotasbcq  |-  ( A. x ( ph  <->  ps )  ->  ( [. ( iota
x ph )  /  y ]. ch  <->  [. ( iota x ps )  /  y ]. ch ) )

Proof of Theorem iotasbcq
StepHypRef Expression
1 iotabi 6261 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( iota x ph )  =  ( iota x ps ) )
2 dfsbcq 2994 . 2  |-  ( ( iota x ph )  =  ( iota x ps )  ->  ( [. ( iota x ph )  /  y ]. ch  <->  [. ( iota x ps )  /  y ]. ch ) )
31, 2syl 17 1  |-  ( A. x ( ph  <->  ps )  ->  ( [. ( iota
x ph )  /  y ]. ch  <->  [. ( iota x ps )  /  y ]. ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1528    = wceq 1624   [.wsbc 2992   iotacio 6250
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 1867  ax-ext 2265
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-clab 2271  df-cleq 2277  df-clel 2280  df-nfc 2409  df-rex 2550  df-sbc 2993  df-uni 3829  df-iota 6252
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