Theorem iotaequ 45167

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 6510	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 ↔ 𝑥 = 𝑦) → (℩𝑥𝑥 = 𝑦) = 𝑦)
2		biid 264	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑥 = 𝑦)
3	1, 2	mpg 1826	1 ⊢ (℩𝑥𝑥 = 𝑦) = 𝑦

This proof depends on syntax axioms:   ↔ wb 209   = wceq 1569  ℩cio 6490

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1572  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-v 3456  df-un 3909  df-ss 3921  df-sn 4589  df-pr 4591  df-uni 4872  df-iota 6492

This theorem is used by: (None)