Theorem riotass 6285

Description: Restriction of a unique element to a smaller class. (Contributed by NM, 19-Oct-2005.) (Revised by Mario Carneiro, 24-Dec-2016.)

Assertion

Ref	Expression
riotass

Distinct variable groups:   ,   ,

Proof of Theorem riotass

Step	Hyp	Ref	Expression
1		reuss 3778	. . . 4
2		riotasbc 6273	. . . 4
3	1, 2	syl 16	. . 3
4		simp1 996	. . . . 5
5		riotacl 6272	. . . . . 6
6	1, 5	syl 16	. . . . 5
7	4, 6	sseldd 3504	. . . 4
8		simp3 998	. . . 4
9		nfriota1 6264	. . . . 5
10	9	nfsbc1 3346	. . . . 5
11		sbceq1a 3338	. . . . 5
12	9, 10, 11	riota2f 6279	. . . 4
13	7, 8, 12	syl2anc 661	. . 3
14	3, 13	mpbid 210	. 2
15	14	eqcomd 2465	1

Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  e.wcel 1818  E.wrex 2808  E!wreu 2809  [.wsbc 3327  C_wss 3475  iota_crio 6256

This theorem is referenced by:  moriotass  6286

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