Theorem iotaequ 45240

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 6511	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2		biid 264	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦)
3	1, 2	mpg 1830	1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦

This proof depends on syntax axioms:   ↔ wb 209   = wceq 1570  ℩cio 6491

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3455  df-un 3907  df-ss 3919  df-sn 4588  df-pr 4590  df-uni 4871  df-iota 6493

This theorem is used by: (None)