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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
StepHypRef Expression
1 reuss 3778 . . . 4
2 riotasbc 6273 . . . 4
31, 2syl 16 . . 3
4 simp1 996 . . . . 5
5 riotacl 6272 . . . . . 6
61, 5syl 16 . . . . 5
74, 6sseldd 3504 . . . 4
8 simp3 998 . . . 4
9 nfriota1 6264 . . . . 5
109nfsbc1 3346 . . . . 5
11 sbceq1a 3338 . . . . 5
129, 10, 11riota2f 6279 . . . 4
137, 8, 12syl2anc 661 . . 3
143, 13mpbid 210 . 2
1514eqcomd 2465 1
 Colors of variables: wff setvar class 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
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