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Theorem riotass2 6291
 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:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem riotass2
StepHypRef Expression
1 reuss2 3754 . . . 4
2 simplr 761 . . . 4
3 riotasbc 6280 . . . . 5
4 riotacl 6279 . . . . . 6
5 rspsbc 3379 . . . . . . 7
6 sbcimg 3342 . . . . . . 7
75, 6sylibd 218 . . . . . 6
84, 7syl 17 . . . . 5
93, 8mpid 43 . . . 4
101, 2, 9sylc 63 . . 3
111, 4syl 17 . . . . 5
12 ssel 3459 . . . . . 6
1312ad2antrr 731 . . . . 5
1411, 13mpd 15 . . . 4
15 simprr 765 . . . 4
16 nfriota1 6272 . . . . 5
1716nfsbc1 3319 . . . . 5
18 sbceq1a 3311 . . . . 5
1916, 17, 18riota2f 6286 . . . 4
2014, 15, 19syl2anc 666 . . 3
2110, 20mpbid 214 . 2
2221eqcomd 2431 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371   wceq 1438   wcel 1869  wral 2776  wrex 2777  wreu 2778  wsbc 3300   wss 3437  crio 6264 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-eu 2270  df-mo 2271  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ral 2781  df-rex 2782  df-reu 2783  df-rab 2785  df-v 3084  df-sbc 3301  df-un 3442  df-in 3444  df-ss 3451  df-sn 3998  df-pr 4000  df-uni 4218  df-iota 5563  df-riota 6265 This theorem is referenced by:  fisupcl  7989  quotlem  23245  adjbdln  27728  rexdiv  28396  cdlemefrs32fva  33930
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