Theorem iotaequ 44411

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 6484	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2		biid 261	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦)
3	1, 2	mpg 1797	1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦

Syntax hints:   ↔ wb 206   = wceq 1540  ℩cio 6464

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-un 3921  df-ss 3933  df-sn 4592  df-pr 4594  df-uni 4874  df-iota 6466

This theorem is referenced by: (None)