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Theorem iotaequ 39470
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 6098 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2 biid 253 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1898 1 (℩𝑥𝑥 = 𝑦) = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wb 198   = wceq 1658  cio 6085
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2804
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2813  df-cleq 2819  df-clel 2822  df-nfc 2959  df-rex 3124  df-v 3417  df-sbc 3664  df-un 3804  df-sn 4399  df-pr 4401  df-uni 4660  df-iota 6087
This theorem is referenced by: (None)
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