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Theorem reupick 3215
Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by NM, 21-Aug-1999.)
Assertion
Ref Expression
reupick  C_
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem reupick
StepHypRef Expression
1 ssel 2933 . . 3 
C_
21ad2antrr 457 . 2  C_
3 df-rex 2306 . . . . . 6
4 df-reu 2307 . . . . . 6
53, 4anbi12i 433 . . . . 5
61ancrd 309 . . . . . . . . . . 11 
C_
76anim1d 319 . . . . . . . . . 10 
C_
8 an32 496 . . . . . . . . . 10
97, 8syl6ib 150 . . . . . . . . 9 
C_
109eximdv 1757 . . . . . . . 8 
C_
11 eupick 1976 . . . . . . . . 9
1211ex 108 . . . . . . . 8
1310, 12syl9 66 . . . . . . 7 
C_
1413com23 72 . . . . . 6 
C_
1514imp32 244 . . . . 5  C_
165, 15sylan2b 271 . . . 4  C_
1716expcomd 1327 . . 3  C_
1817imp 115 . 2  C_
192, 18impbid 120 1  C_
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wex 1378   wcel 1390  weu 1897  wrex 2301  wreu 2302    C_ wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-rex 2306  df-reu 2307  df-in 2918  df-ss 2925
This theorem is referenced by: (None)
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