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Theorem iotasbcq 40186
Description: Theorem *14.272 in [WhiteheadRussell] p. 193. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotasbcq (∀𝑥(𝜑𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒[(℩𝑥𝜓) / 𝑦]𝜒))

Proof of Theorem iotasbcq
StepHypRef Expression
1 iotabi 6163 . 2 (∀𝑥(𝜑𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
21sbceq1d 3688 1 (∀𝑥(𝜑𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒[(℩𝑥𝜓) / 𝑦]𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  wal 1505  [wsbc 3683  cio 6152
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-ext 2750
This theorem depends on definitions:  df-bi 199  df-an 388  df-ex 1743  df-sb 2016  df-clab 2759  df-cleq 2771  df-clel 2846  df-rex 3094  df-sbc 3684  df-uni 4714  df-iota 6154
This theorem is referenced by: (None)
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