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Theorem iotaequ 41304
 Description: Theorem *14.2 in [WhiteheadRussell] p. 189. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
iotaequ (℩𝑥𝑥 = 𝑦) = 𝑦
Distinct variable group:   𝑥,𝑦

Proof of Theorem iotaequ
StepHypRef Expression
1 iotaval 6306 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2 biid 264 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1799 1 (℩𝑥𝑥 = 𝑦) = 𝑦
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   = wceq 1538  ℩cio 6289 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3444  df-sbc 3723  df-un 3888  df-in 3890  df-ss 3900  df-sn 4529  df-pr 4531  df-uni 4805  df-iota 6291 This theorem is referenced by: (None)
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