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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
StepHypRef 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
75, 6sylibd 214 . . . . . 6
84, 7syl 16 . . . . 5
93, 8mpid 41 . . . 4
101, 2, 9sylc 60 . . 3
111, 4syl 16 . . . . 5
12 ssel 3497 . . . . . 6
1312ad2antrr 725 . . . . 5
1411, 13mpd 15 . . . 4
15 simprr 757 . . . 4
16 nfriota1 6264 . . . . 5
1716nfsbc1 3346 . . . . 5
18 sbceq1a 3338 . . . . 5
1916, 17, 18riota2f 6279 . . . 4
2014, 15, 19syl2anc 661 . . 3
2110, 20mpbid 210 . 2
2221eqcomd 2465 1
 Colors of variables: wff setvar class 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
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