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Theorem iotasbcq 44456
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 6527 . 2 (∀𝑥(𝜑𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
21sbceq1d 3793 1 (∀𝑥(𝜑𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒[(℩𝑥𝜓) / 𝑦]𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wal 1538  [wsbc 3788  cio 6512
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-sbc 3789  df-ss 3968  df-uni 4908  df-iota 6514
This theorem is referenced by: (None)
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