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Theorem reupick2 3759
 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:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem reupick2
StepHypRef Expression
1 ancr 551 . . . . . 6
21ralimi 2818 . . . . 5
3 rexim 2890 . . . . 5
42, 3syl 17 . . . 4
5 reupick3 3758 . . . . . 6
653exp 1204 . . . . 5
76com12 32 . . . 4
84, 7syl6 34 . . 3
983imp1 1218 . 2
10 rsp 2791 . . . 4
11103ad2ant1 1026 . . 3
1211imp 430 . 2
139, 12impbid 193 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370   w3a 982   wcel 1868  wral 2775  wrex 2776  wreu 2777 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-12 1905  ax-13 2053 This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984  df-ex 1660  df-nf 1664  df-eu 2269  df-mo 2270  df-ral 2780  df-rex 2781  df-reu 2782 This theorem is referenced by:  grpoidval  25927  grpoidinv2  25929  grpoinv  25938
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