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Theorem iotasbcq 27637
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 5228 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( iota x ph )  =  ( iota x ps ) )
2 dfsbcq 2993 . 2  |-  ( ( iota x ph )  =  ( iota x ps )  ->  ( [. ( iota x ph )  /  y ]. ch  <->  [. ( iota x ps )  /  y ]. ch ) )
31, 2syl 15 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 176   A.wal 1527    = wceq 1623   [.wsbc 2991   iotacio 5217
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-sbc 2992  df-uni 3828  df-iota 5219
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