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Theorem riotass 6294
 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:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem riotass
StepHypRef Expression
1 reuss 3760 . . . 4
2 riotasbc 6282 . . . 4
31, 2syl 17 . . 3
4 simp1 1005 . . . . 5
5 riotacl 6281 . . . . . 6
61, 5syl 17 . . . . 5
74, 6sseldd 3471 . . . 4
8 simp3 1007 . . . 4
9 nfriota1 6274 . . . . 5
109nfsbc1 3324 . . . . 5
11 sbceq1a 3316 . . . . 5
129, 10, 11riota2f 6288 . . . 4
137, 8, 12syl2anc 665 . . 3
143, 13mpbid 213 . 2
1514eqcomd 2437 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   w3a 982   wceq 1437   wcel 1870  wrex 2783  wreu 2784  wsbc 3305   wss 3442  crio 6266 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rex 2788  df-reu 2789  df-rab 2791  df-v 3089  df-sbc 3306  df-un 3447  df-in 3449  df-ss 3456  df-sn 4003  df-pr 4005  df-uni 4223  df-iota 5565  df-riota 6267 This theorem is referenced by:  moriotass  6295
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