Theorem nfuni 4807

Description: Bound-variable hypothesis builder for union. (Contributed by NM, 30-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)

Hypothesis

Ref	Expression
nfuni.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfuni	⊢ Ⅎ𝑥∪ 𝐴

Proof of Theorem nfuni

Step	Hyp	Ref	Expression
1		nfuni.1	. 2 ⊢ Ⅎ𝑥𝐴
2		id 22	. . 3 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥𝐴)
3	2	nfunid 4806	. 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥∪ 𝐴)
4	1, 3	ax-mp 5	1 ⊢ Ⅎ𝑥∪ 𝐴

Syntax hints:  Ⅎwnfc 2936  ∪ cuni 4800

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rex 3112  df-uni 4801

This theorem is referenced by:  nfiota1  6285  nfwrecs  7932  nfsup  8899  ptunimpt  22200  disjabrex  30345  disjabrexf  30346  fnpreimac  30434  nfesum1  31409  nfesum2  31410  bnj1398  32416  bnj1446  32427  bnj1447  32428  bnj1448  32429  bnj1466  32435  bnj1467  32436  bnj1519  32447  bnj1520  32448  bnj1525  32451  bnj1523  32453  dfon2lem3  33143  nffrecs  33233  mptsnunlem  34755  ptrest  35056  heibor1  35248  nfunidALT2  36265  nfunidALT  36266  disjinfi  41820  stoweidlem28  42670  stoweidlem59  42701  fourierdlem80  42828  smfresal  43420  smfpimbor1lem2  43431  nfafv2  43774  nfsetrecs  45216