Theorem iotaequ 44943

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

Step	Hyp	Ref	Expression
1		iotaval 6480	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2		biid 263	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦)
3	1, 2	mpg 1807	1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦

Syntax hints:   ↔ wb 208   = wceq 1550  ℩cio 6460

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1805  ax-4 1819  ax-5 1920  ax-6 1977  ax-7 2018  ax-8 2134  ax-9 2142  ax-ext 2724

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 857  df-tru 1553  df-ex 1790  df-sb 2081  df-clab 2731  df-cleq 2744  df-clel 2827  df-v 3446  df-un 3900  df-ss 3912  df-sn 4573  df-pr 4575  df-uni 4856  df-iota 6462

This theorem is referenced by: (None)