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

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)
 Copyright terms: Public domain W3C validator