Theorem nfiota1 6475

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 6474	. 2 ⊢ (℩𝑥𝜑) = ∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)}
2		nfaba1 2931	. . 3 ⊢ Ⅎ𝑥{𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)}
3	2	nfuni 4871	. 2 ⊢ Ⅎ𝑥∪ {𝑦 ∣ ∀𝑥(𝜑 ↔ 𝑥 = 𝑦)}
4	1, 3	nfcxfr 2921	1 ⊢ Ⅎ𝑥(℩𝑥𝜑)

Syntax hints:   ↔ wb 208  ∀wal 1557  {cab 2739  Ⅎwnfc 2908  ∪ cuni 4864  ℩cio 6471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-10 2174  ax-11 2190  ax-12 2211  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1562  df-ex 1799  df-nf 1803  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-nfc 2910  df-ral 3076  df-rex 3086  df-v 3455  df-ss 3921  df-sn 4582  df-uni 4865  df-iota 6473

This theorem is referenced by:  iota2df  6504  sniota  6508  opabiota  6945  nfriota1  7356  nfriotadw  7357  nfriotad  7360  erovlem  8790  nosupbnd2  27757  noinfbnd2  27772  bnj1366  35088