Theorem eusvnfb 4648

Description: Two ways to say that A(x) is a set expression that does not depend on . (Contributed by Mario Carneiro, 18-Nov-2016.)

Assertion

Ref	Expression
eusvnfb

Distinct variable groups:   ,   ,

Proof of Theorem eusvnfb

Step	Hyp	Ref	Expression
1		eusvnf 4647	. . 3
2		euex 2308	. . . 4
3		eqvisset 3117	. . . . . 6
4	3	sps 1865	. . . . 5
5	4	exlimiv 1722	. . . 4
6	2, 5	syl 16	. . 3
7	1, 6	jca 532	. 2
8		isset 3113	. . . . 5
9		nfcvd 2620	. . . . . . . 8
10		id 22	. . . . . . . 8
11	9, 10	nfeqd 2626	. . . . . . 7
12	11	nfrd 1875	. . . . . 6
13	12	eximdv 1710	. . . . 5
14	8, 13	syl5bi 217	. . . 4
15	14	imp 429	. . 3
16		eusv1 4646	. . 3
17	15, 16	sylibr 212	. 2
18	7, 17	impbii 188	1

Syntax hints:  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  E!weu 2282  F/_wnfc 2605  cvv 3109

This theorem is referenced by:  eusv2nf  4650  eusv2  4651

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785