Theorem iotaequ 44379

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 6498	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2		biid 261	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦)
3	1, 2	mpg 1796	1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦

Syntax hints:   ↔ wb 206   = wceq 1539  ℩cio 6478

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-v 3459  df-un 3929  df-ss 3941  df-sn 4600  df-pr 4602  df-uni 4881  df-iota 6480

This theorem is referenced by: (None)