Theorem reupick 3781

Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by NM, 21-Aug-1999.)

Assertion

Ref	Expression
reupick

Distinct variable groups:   ,   ,

Proof of Theorem reupick

Step	Hyp	Ref	Expression
1		ssel 3497	. . 3
2	1	ad2antrr 725	. 2
3		df-rex 2813	. . . . . 6
4		df-reu 2814	. . . . . 6
5	3, 4	anbi12i 697	. . . . 5
6	1	ancrd 554	. . . . . . . . . . 11
7	6	anim1d 564	. . . . . . . . . 10
8		an32 798	. . . . . . . . . 10
9	7, 8	syl6ib 226	. . . . . . . . 9
10	9	eximdv 1710	. . . . . . . 8
11		eupick 2358	. . . . . . . . 9
12	11	ex 434	. . . . . . . 8
13	10, 12	syl9 71	. . . . . . 7
14	13	com23 78	. . . . . 6
15	14	imp32 433	. . . . 5
16	5, 15	sylan2b 475	. . . 4
17	16	expcomd 438	. . 3
18	17	imp 429	. 2
19	2, 18	impbid 191	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  E.wex 1612  e.wcel 1818  E!weu 2282  E.wrex 2808  E!wreu 2809  C_wss 3475

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-an 371  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-rex 2813  df-reu 2814  df-in 3482  df-ss 3489