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Theorem iotaequ 41720
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 6354 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2 biid 264 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1805 1 (℩𝑥𝑥 = 𝑦) = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wb 209   = wceq 1543  cio 6336
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2158  ax-12 2175  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-ex 1788  df-nf 1792  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3410  df-un 3871  df-in 3873  df-ss 3883  df-sn 4542  df-pr 4544  df-uni 4820  df-iota 6338
This theorem is referenced by: (None)
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