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Theorem iotasbcq 38955
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 5898 . 2 (∀𝑥(𝜑𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
21sbceq1d 3473 1 (∀𝑥(𝜑𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒[(℩𝑥𝜓) / 𝑦]𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1521  [wsbc 3468  cio 5887
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rex 2947  df-sbc 3469  df-uni 4469  df-iota 5889
This theorem is referenced by: (None)
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