Theorem nfuni 4877

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 4876	. 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥∪ 𝐴)
4	1, 3	ax-mp 5	1 ⊢ Ⅎ𝑥∪ 𝐴

Syntax hints:  Ⅎwnfc 2882  ∪ cuni 4870

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-ex 1782  df-nf 1786  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-nfc 2884  df-ral 3061  df-rex 3070  df-uni 4871

This theorem is referenced by:  nfiota1  6455  nffrecs  8219  nfwrecsOLD  8253  nfsup  9396  ptunimpt  22983  disjabrex  31567  disjabrexf  31568  fnpreimac  31654  nfesum1  32728  nfesum2  32729  bnj1398  33735  bnj1446  33746  bnj1447  33747  bnj1448  33748  bnj1466  33754  bnj1467  33755  bnj1519  33766  bnj1520  33767  bnj1525  33770  bnj1523  33772  dfon2lem3  34446  mptsnunlem  35882  ptrest  36150  heibor1  36342  nfunidALT2  37504  nfunidALT  37505  disjinfi  43534  stoweidlem28  44389  stoweidlem59  44420  fourierdlem80  44547  saliinclf  44687  smfresal  45149  smfpimbor1lem2  45160  nfafv2  45570  nfsetrecs  47251