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Theorem iotaequ 44384
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 6529 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2 biid 261 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1792 1 (℩𝑥𝑥 = 𝑦) = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wb 206   = wceq 1535  cio 6508
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-ext 2704
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1538  df-ex 1775  df-sb 2061  df-clab 2711  df-cleq 2725  df-clel 2812  df-v 3479  df-un 3968  df-ss 3980  df-sn 4631  df-pr 4633  df-uni 4915  df-iota 6510
This theorem is referenced by: (None)
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