Theorem nfiota1 4342

Description: Bound-variable hypothesis builder for the ℩ class. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)

Assertion

Ref	Expression
nfiota1	⊢ Ⅎx(℩xφ)

Proof of Theorem nfiota1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfiota2 4341	. 2 ⊢ (℩xφ) = ∪{y ∣ ∀x(φ ↔ x = y)}
2		nfaba1 2495	. . 3 ⊢ Ⅎx{y ∣ ∀x(φ ↔ x = y)}
3	2	nfuni 3898	. 2 ⊢ Ⅎx∪{y ∣ ∀x(φ ↔ x = y)}
4	1, 3	nfcxfr 2487	1 ⊢ Ⅎx(℩xφ)

Syntax hints:   ↔ wb 176  ∀wal 1540   = wceq 1642  {cab 2339  Ⅎwnfc 2477  ∪cuni 3892  ℩cio 4338

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-ral 2620  df-rex 2621  df-sn 3742  df-uni 3893  df-iota 4340

This theorem is referenced by:  iota2df  4366  sniota  4370