Theorem reuhypd 4679

Description: A theorem useful for eliminating the restricted existential uniqueness hypotheses in riotaxfrd 6288. (Contributed by NM, 16-Jan-2012.)

Hypotheses

Ref	Expression
reuhypd.1
reuhypd.2

Assertion

Ref	Expression
reuhypd

Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem reuhypd

Step	Hyp	Ref	Expression
1		reuhypd.1	. . . . 5
2		elex 3118	. . . . 5
3	1, 2	syl 16	. . . 4
4		eueq 3271	. . . 4
5	3, 4	sylib 196	. . 3
6		eleq1 2529	. . . . . . 7
7	1, 6	syl5ibrcom 222	. . . . . 6
8	7	pm4.71rd 635	. . . . 5
9		reuhypd.2	. . . . . . 7
10	9	3expa 1196	. . . . . 6
11	10	pm5.32da 641	. . . . 5
12	8, 11	bitr4d 256	. . . 4
13	12	eubidv 2304	. . 3
14	5, 13	mpbid 210	. 2
15		df-reu 2814	. 2
16	14, 15	sylibr 212	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  E!weu 2282  E!wreu 2809  cvv 3109

This theorem is referenced by:  reuhyp  4680  riotaocN  34934

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-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-reu 2814  df-v 3111