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Theorem iotasbcq 40646
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 6320 . 2 (∀𝑥(𝜑𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
21sbceq1d 3774 1 (∀𝑥(𝜑𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒[(℩𝑥𝜓) / 𝑦]𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wal 1526  [wsbc 3769  cio 6305
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-rex 3141  df-sbc 3770  df-uni 4831  df-iota 6307
This theorem is referenced by: (None)
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