Theorem nfiota1 6450

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 6449	. 2 ⊢ (℩𝑥𝜑) = ∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)}
2		nfaba1 2910	. . 3 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)}
3	2	nfuni 4852	. 2 ⊢ Ⅎ𝑥∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)}
4	1, 3	nfcxfr 2900	1 ⊢ Ⅎ𝑥(℩𝑥𝜑)

Syntax hints:   ↔ wb 207  ∀wal 1545  {cab 2718  Ⅎwnfc 2887  ∪ cuni 4845  ℩cio 6446

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-10 2152  ax-11 2168  ax-12 2189  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-nf 1791  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-nfc 2889  df-ral 3055  df-rex 3065  df-v 3434  df-ss 3907  df-sn 4563  df-uni 4846  df-iota 6448

This theorem is referenced by:  iota2df  6479  sniota  6483  opabiota  6916  nfriota1  7327  nfriotadw  7328  nfriotad  7331  erovlem  8757  nosupbnd2  27705  noinfbnd2  27720  bnj1366  35018