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Theorem iotasbcq 37460
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 5760 . 2 (∀𝑥(𝜑𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
21sbceq1d 3403 1 (∀𝑥(𝜑𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒[(℩𝑥𝜓) / 𝑦]𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wal 1472  [wsbc 3398  cio 5749
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2032  ax-13 2229  ax-ext 2586
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2593  df-cleq 2599  df-clel 2602  df-nfc 2736  df-rex 2898  df-sbc 3399  df-uni 4364  df-iota 5751
This theorem is referenced by: (None)
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