Theorem nfuni 4838

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 4837	. 2 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥∪ 𝐴)
4	1, 3	ax-mp 5	1 ⊢ Ⅎ𝑥∪ 𝐴

Syntax hints:  Ⅎwnfc 2961  ∪ cuni 4831

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ex 1777  df-nf 1781  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-ral 3143  df-rex 3144  df-uni 4832

This theorem is referenced by:  nfiota1  6310  nfwrecs  7943  nfsup  8909  ptunimpt  22197  disjabrex  30326  disjabrexf  30327  fnpreimac  30410  nfesum1  31294  nfesum2  31295  bnj1398  32301  bnj1446  32312  bnj1447  32313  bnj1448  32314  bnj1466  32320  bnj1467  32321  bnj1519  32332  bnj1520  32333  bnj1525  32336  bnj1523  32338  dfon2lem3  33025  nffrecs  33115  mptsnunlem  34613  ptrest  34885  heibor1  35082  nfunidALT2  36099  nfunidALT  36100  disjinfi  41447  stoweidlem28  42307  stoweidlem59  42338  fourierdlem80  42465  smfresal  43057  smfpimbor1lem2  43068  nfafv2  43411  nfsetrecs  44783