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Theorem iotasbcq 27616
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 5429 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( iota x ph )  =  ( iota x ps ) )
2 dfsbcq 3165 . 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 178   A.wal 1550    = wceq 1653   [.wsbc 3163   iotacio 5418
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-sbc 3164  df-uni 4018  df-iota 5420
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