Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  reupick Structured version   Unicode version

Theorem reupick 3627
 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 3344 . . 3
3 df-rex 2713 . . . . . 6
4 df-reu 2714 . . . . . 6
53, 4anbi12i 680 . . . . 5
61ancrd 539 . . . . . . . . . . 11
76anim1d 549 . . . . . . . . . 10
8 an32 775 . . . . . . . . . 10
97, 8syl6ib 219 . . . . . . . . 9
109eximdv 1633 . . . . . . . 8
11 eupick 2346 . . . . . . . . 9
1211ex 425 . . . . . . . 8
1310, 12syl9 69 . . . . . . 7
1413com23 75 . . . . . 6
1514imp32 424 . . . . 5
165, 15sylan2b 463 . . . 4
1716exp3acom23 1382 . . 3
1817imp 420 . 2
192, 18impbid 185 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wcel 1726  weu 2283  wrex 2708  wreu 2709   wss 3322 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-rex 2713  df-reu 2714  df-in 3329  df-ss 3336
 Copyright terms: Public domain W3C validator