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Theorem reupick 3781
Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by NM, 21-Aug-1999.)
Assertion
Ref Expression
reupick
Distinct variable groups:   ,   ,

Proof of Theorem reupick
StepHypRef Expression
1 ssel 3497 . . 3
21ad2antrr 725 . 2
3 df-rex 2813 . . . . . 6
4 df-reu 2814 . . . . . 6
53, 4anbi12i 697 . . . . 5
61ancrd 554 . . . . . . . . . . 11
76anim1d 564 . . . . . . . . . 10
8 an32 798 . . . . . . . . . 10
97, 8syl6ib 226 . . . . . . . . 9
109eximdv 1710 . . . . . . . 8
11 eupick 2358 . . . . . . . . 9
1211ex 434 . . . . . . . 8
1310, 12syl9 71 . . . . . . 7
1413com23 78 . . . . . 6
1514imp32 433 . . . . 5
165, 15sylan2b 475 . . . 4
1716expcomd 438 . . 3
1817imp 429 . 2
192, 18impbid 191 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  E.wex 1612  e.wcel 1818  E!weu 2282  E.wrex 2808  E!wreu 2809  C_wss 3475
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-rex 2813  df-reu 2814  df-in 3482  df-ss 3489
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