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Theorem iotaequ 44426
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 6530 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2 biid 261 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1797 1 (℩𝑥𝑥 = 𝑦) = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wb 206   = wceq 1540  cio 6510
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 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-un 3955  df-ss 3967  df-sn 4625  df-pr 4627  df-uni 4906  df-iota 6512
This theorem is referenced by: (None)
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