New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  reupick Unicode version

Theorem reupick 3539
 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 3267 . . 3
3 df-rex 2620 . . . . . 6
4 df-reu 2621 . . . . . 6
53, 4anbi12i 678 . . . . 5
61ancrd 537 . . . . . . . . . . 11
76anim1d 547 . . . . . . . . . 10
8 an32 773 . . . . . . . . . 10
97, 8syl6ib 217 . . . . . . . . 9
109eximdv 1622 . . . . . . . 8
11 eupick 2267 . . . . . . . . 9
1211ex 423 . . . . . . . 8
1310, 12syl9 66 . . . . . . 7
1413com23 72 . . . . . 6
1514imp32 422 . . . . 5
165, 15sylan2b 461 . . . 4
1716exp3acom23 1372 . . 3
1817imp 418 . 2
192, 18impbid 183 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wcel 1710  weu 2204  wrex 2615  wreu 2616   wss 3257 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-reu 2621  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator