 Mathbox for Andrew Salmon < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  iotaequ Structured version   Visualization version   GIF version

Theorem iotaequ 37652
 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 5779 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2 biid 250 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1715 1 (℩𝑥𝑥 = 𝑦) = 𝑦
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 195   = wceq 1475  ℩cio 5766 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-v 3175  df-sbc 3403  df-un 3545  df-sn 4126  df-pr 4128  df-uni 4373  df-iota 5768 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator