Theorem riotass2 6284

Description: Restriction of a unique element to a smaller class. (Contributed by NM, 21-Aug-2011.) (Revised by NM, 22-Mar-2013.)

Assertion

Ref	Expression
riotass2

Distinct variable groups:   ,   ,

Proof of Theorem riotass2

Step	Hyp	Ref	Expression
1		reuss2 3777	. . . 4
2		simplr 755	. . . 4
3		riotasbc 6273	. . . . 5
4		riotacl 6272	. . . . . 6
5		rspsbc 3417	. . . . . . 7
6		sbcimg 3369	. . . . . . 7
7	5, 6	sylibd 214	. . . . . 6
8	4, 7	syl 16	. . . . 5
9	3, 8	mpid 41	. . . 4
10	1, 2, 9	sylc 60	. . 3
11	1, 4	syl 16	. . . . 5
12		ssel 3497	. . . . . 6
13	12	ad2antrr 725	. . . . 5
14	11, 13	mpd 15	. . . 4
15		simprr 757	. . . 4
16		nfriota1 6264	. . . . 5
17	16	nfsbc1 3346	. . . . 5
18		sbceq1a 3338	. . . . 5
19	16, 17, 18	riota2f 6279	. . . 4
20	14, 15, 19	syl2anc 661	. . 3
21	10, 20	mpbid 210	. 2
22	21	eqcomd 2465	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  E.wrex 2808  E!wreu 2809  [.wsbc 3327  C_wss 3475  iota_crio 6256

This theorem is referenced by:  fisupcl  7948  quotlem  22696  adjbdln  27002  rexdiv  27622  cdlemefrs32fva  36126

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-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-rab 2816  df-v 3111  df-sbc 3328  df-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-riota 6257