Theorem reu8 3295

Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.)

Hypothesis

Ref	Expression
rmo4.1

Assertion

Ref	Expression
reu8

Distinct variable groups:   ,,   ,   ,

Proof of Theorem reu8

Step	Hyp	Ref	Expression
1		rmo4.1	. . 3
2	1	cbvreuv 3086	. 2
3		reu6 3288	. 2
4		dfbi2 628	. . . . 5
5	4	ralbii 2888	. . . 4
6		ancom 450	. . . . . 6
7		equcom 1794	. . . . . . . . . 10
8	7	imbi2i 312	. . . . . . . . 9
9	8	ralbii 2888	. . . . . . . 8
10	9	a1i 11	. . . . . . 7
11		biimt 335	. . . . . . . 8
12		df-ral 2812	. . . . . . . . 9
13		bi2.04 361	. . . . . . . . . 10
14	13	albii 1640	. . . . . . . . 9
15		vex 3112	. . . . . . . . . 10
16		eleq1 2529	. . . . . . . . . . . . 13
17	16, 1	imbi12d 320	. . . . . . . . . . . 12
18	17	bicomd 201	. . . . . . . . . . 11
19	18	equcoms 1795	. . . . . . . . . 10
20	15, 19	ceqsalv 3137	. . . . . . . . 9
21	12, 14, 20	3bitrri 272	. . . . . . . 8
22	11, 21	syl6bb 261	. . . . . . 7
23	10, 22	anbi12d 710	. . . . . 6
24	6, 23	syl5bb 257	. . . . 5
25		r19.26 2984	. . . . 5
26	24, 25	syl6rbbr 264	. . . 4
27	5, 26	syl5bb 257	. . 3
28	27	rexbiia 2958	. 2
29	2, 3, 28	3bitri 271	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  e.wcel 1818  A.wral 2807  E.wrex 2808  E!wreu 2809

This theorem is referenced by:  reuccats1  12706  reumodprminv  14329  grpinveu  16084  grpoideu  25211  grpoinveu  25224  cvmlift3lem2  28765

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-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-rex 2813  df-reu 2814  df-v 3111