Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  riotass2 Structured version   Unicode version

Theorem riotass2 6579
 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 3623 . . . 4
2 simplr 733 . . . 4
3 riotasbc 6567 . . . . 5
4 riotacl 6566 . . . . . 6
5 rspsbc 3241 . . . . . . 7
6 sbcimg 3204 . . . . . . 7
75, 6sylibd 207 . . . . . 6
84, 7syl 16 . . . . 5
93, 8mpid 40 . . . 4
101, 2, 9sylc 59 . . 3
111, 4syl 16 . . . . 5
12 ssel 3344 . . . . . 6
1312ad2antrr 708 . . . . 5
1411, 13mpd 15 . . . 4
15 simprr 735 . . . 4
16 nfriota1 6559 . . . . 5
1716nfsbc1 3181 . . . . 5
18 sbceq1a 3173 . . . . 5
1916, 17, 18riota2f 6573 . . . 4
2014, 15, 19syl2anc 644 . . 3
2110, 20mpbid 203 . 2
2221eqcomd 2443 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707  wrex 2708  wreu 2709  wsbc 3163   wss 3322  crio 6544 This theorem is referenced by:  fisupcl  7474  quotlem  20219  adjbdln  23588  rexdiv  24174  cdlemefrs32fva  31199 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-riota 6551
 Copyright terms: Public domain W3C validator