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Theorem reupick2 3783
Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by Mario Carneiro, 15-Dec-2013.) (Proof shortened by Mario Carneiro, 19-Nov-2016.)
Assertion
Ref Expression
reupick2
Distinct variable group:   ,

Proof of Theorem reupick2
StepHypRef Expression
1 ancr 549 . . . . . 6
21ralimi 2850 . . . . 5
3 rexim 2922 . . . . 5
42, 3syl 16 . . . 4
5 reupick3 3782 . . . . . 6
653exp 1195 . . . . 5
76com12 31 . . . 4
84, 7syl6 33 . . 3
983imp1 1209 . 2
10 rsp 2823 . . . 4
11103ad2ant1 1017 . . 3
1211imp 429 . 2
139, 12impbid 191 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  e.wcel 1818  A.wral 2807  E.wrex 2808  E!wreu 2809
This theorem is referenced by:  grpoidval  25218  grpoidinv2  25220  grpoinv  25229
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-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287  df-ral 2812  df-rex 2813  df-reu 2814
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