Theorem nfuni 4881

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 4880	. 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥∪ 𝐴)
4	1, 3	ax-mp 5	1 ⊢ Ⅎ𝑥∪ 𝐴

Syntax hints:  Ⅎwnfc 2877  ∪ cuni 4874

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 2702

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 2709  df-cleq 2722  df-clel 2804  df-nfc 2879  df-ral 3046  df-rex 3055  df-uni 4875

This theorem is referenced by:  nfiota1  6469  nffrecs  8265  nfsup  9409  ptunimpt  23489  disjabrex  32518  disjabrexf  32519  fnpreimac  32602  nfesum1  34037  nfesum2  34038  bnj1398  35031  bnj1446  35042  bnj1447  35043  bnj1448  35044  bnj1466  35050  bnj1467  35051  bnj1519  35062  bnj1520  35063  bnj1525  35066  bnj1523  35068  dfon2lem3  35780  mptsnunlem  37333  ptrest  37620  heibor1  37811  nfunidALT2  38969  nfunidALT  38970  disjinfi  45193  stoweidlem28  46033  stoweidlem59  46064  fourierdlem80  46191  saliinclf  46331  smfresal  46793  smfpimbor1lem2  46804  nfafv2  47223  nfsetrecs  49679