Theorem nfuni 4916

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 4915	. 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥∪ 𝐴)
4	1, 3	ax-mp 5	1 ⊢ Ⅎ𝑥∪ 𝐴

Syntax hints:  Ⅎwnfc 2884  ∪ cuni 4909

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-ral 3063  df-rex 3072  df-uni 4910

This theorem is referenced by:  nfiota1  6498  nffrecs  8268  nfwrecsOLD  8302  nfsup  9446  ptunimpt  23099  disjabrex  31813  disjabrexf  31814  fnpreimac  31896  nfesum1  33038  nfesum2  33039  bnj1398  34045  bnj1446  34056  bnj1447  34057  bnj1448  34058  bnj1466  34064  bnj1467  34065  bnj1519  34076  bnj1520  34077  bnj1525  34080  bnj1523  34082  dfon2lem3  34757  mptsnunlem  36219  ptrest  36487  heibor1  36678  nfunidALT2  37839  nfunidALT  37840  disjinfi  43891  stoweidlem28  44744  stoweidlem59  44775  fourierdlem80  44902  saliinclf  45042  smfresal  45504  smfpimbor1lem2  45515  nfafv2  45926  nfsetrecs  47731