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Theorem iotasbcq 26960
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 5310 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( iota x ph )  =  ( iota x ps ) )
2 dfsbcq 3069 . 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 1540    = wceq 1642   [.wsbc 3067   iotacio 5299
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-rex 2625  df-sbc 3068  df-uni 3909  df-iota 5301
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