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Theorem reupick 3727
 Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by NM, 21-Aug-1999.)
Assertion
Ref Expression
reupick
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem reupick
StepHypRef Expression
1 ssel 3426 . . 3
21ad2antrr 732 . 2
3 df-rex 2743 . . . . . 6
4 df-reu 2744 . . . . . 6
53, 4anbi12i 703 . . . . 5
61ancrd 557 . . . . . . . . . . 11
76anim1d 568 . . . . . . . . . 10
8 an32 807 . . . . . . . . . 10
97, 8syl6ib 230 . . . . . . . . 9
109eximdv 1764 . . . . . . . 8
11 eupick 2365 . . . . . . . . 9
1211ex 436 . . . . . . . 8
1310, 12syl9 73 . . . . . . 7
1413com23 81 . . . . . 6
1514imp32 435 . . . . 5
165, 15sylan2b 478 . . . 4
1716expcomd 440 . . 3
1817imp 431 . 2
192, 18impbid 194 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wex 1663   wcel 1887  weu 2299  wrex 2738  wreu 2739   wss 3404 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-rex 2743  df-reu 2744  df-in 3411  df-ss 3418 This theorem is referenced by: (None)
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