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Theorem riotass 6570
 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 3614 . . . 4
2 riotasbc 6557 . . . 4
31, 2syl 16 . . 3
4 simp1 957 . . . . 5
5 riotacl 6556 . . . . . 6
61, 5syl 16 . . . . 5
74, 6sseldd 3341 . . . 4
8 simp3 959 . . . 4
9 nfriota1 6549 . . . . 5
109nfsbc1 3171 . . . . 5
11 sbceq1a 3163 . . . . 5
129, 10, 11riota2f 6563 . . . 4
137, 8, 12syl2anc 643 . . 3
143, 13mpbid 202 . 2
1514eqcomd 2440 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3a 936   wceq 1652   wcel 1725  wrex 2698  wreu 2699  wsbc 3153   wss 3312  crio 6534 This theorem is referenced by:  moriotass  6571 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-riota 6541
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