Theorem nfuni 4874

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 4873	. 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥∪ 𝐴)
4	1, 3	ax-mp 5	1 ⊢ Ⅎ𝑥∪ 𝐴

Syntax hints:  Ⅎwnfc 2876  ∪ cuni 4867

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1780  df-nf 1784  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-nfc 2878  df-ral 3045  df-rex 3054  df-uni 4868

This theorem is referenced by:  nfiota1  6454  nffrecs  8239  nfsup  9378  ptunimpt  23458  disjabrex  32484  disjabrexf  32485  fnpreimac  32568  nfesum1  34003  nfesum2  34004  bnj1398  34997  bnj1446  35008  bnj1447  35009  bnj1448  35010  bnj1466  35016  bnj1467  35017  bnj1519  35028  bnj1520  35029  bnj1525  35032  bnj1523  35034  dfon2lem3  35746  mptsnunlem  37299  ptrest  37586  heibor1  37777  nfunidALT2  38935  nfunidALT  38936  disjinfi  45159  stoweidlem28  45999  stoweidlem59  46030  fourierdlem80  46157  saliinclf  46297  smfresal  46759  smfpimbor1lem2  46770  nfafv2  47192  nfsetrecs  49648