Theorem nfuni 4851

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 4850	. 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥∪ 𝐴)
4	1, 3	ax-mp 5	1 ⊢ Ⅎ𝑥∪ 𝐴

Syntax hints:  Ⅎwnfc 2888  ∪ cuni 4844

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1801  ax-4 1815  ax-5 1916  ax-6 1974  ax-7 2014  ax-8 2111  ax-9 2119  ax-10 2140  ax-11 2157  ax-12 2174  ax-ext 2710

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-ex 1786  df-nf 1790  df-sb 2071  df-clab 2717  df-cleq 2731  df-clel 2817  df-nfc 2890  df-ral 3070  df-rex 3071  df-uni 4845

This theorem is referenced by:  nfiota1  6390  nffrecs  8083  nfwrecsOLD  8117  nfsup  9171  ptunimpt  22727  disjabrex  30900  disjabrexf  30901  fnpreimac  30987  nfesum1  31987  nfesum2  31988  bnj1398  32993  bnj1446  33004  bnj1447  33005  bnj1448  33006  bnj1466  33012  bnj1467  33013  bnj1519  33024  bnj1520  33025  bnj1525  33028  bnj1523  33030  dfon2lem3  33740  mptsnunlem  35488  ptrest  35755  heibor1  35947  nfunidALT2  36962  nfunidALT  36963  disjinfi  42684  stoweidlem28  43523  stoweidlem59  43554  fourierdlem80  43681  smfresal  44273  smfpimbor1lem2  44284  nfafv2  44661  nfsetrecs  46344