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Theorem iotasbcq 27505
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 5386 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( iota x ph )  =  ( iota x ps ) )
2 dfsbcq 3123 . 2  |-  ( ( iota x ph )  =  ( iota x ps )  ->  ( [. ( iota x ph )  /  y ]. ch  <->  [. ( iota x ps )  /  y ]. ch ) )
31, 2syl 16 1  |-  ( A. x ( ph  <->  ps )  ->  ( [. ( iota
x ph )  /  y ]. ch  <->  [. ( iota x ps )  /  y ]. ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1546    = wceq 1649   [.wsbc 3121   iotacio 5375
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rex 2672  df-sbc 3122  df-uni 3976  df-iota 5377
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