Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  isfin2 Structured version   Unicode version

Theorem isfin2 8166
 Description: Definition of a II-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)
Assertion
Ref Expression
isfin2 FinII []
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem isfin2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pweq 3794 . . . 4
21pweqd 3796 . . 3
32raleqdv 2902 . 2 [] []
4 df-fin2 8158 . 2 FinII []
53, 4elab2g 3076 1 FinII []
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725   wne 2598  wral 2697  c0 3620  cpw 3791  cuni 4007   wor 4494   [] crpss 6513  FinIIcfin2 8151 This theorem is referenced by:  fin2i  8167  isfin2-2  8191  ssfin2  8192  enfin2i  8193  fin12  8285  fin1a2s  8286 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-v 2950  df-in 3319  df-ss 3326  df-pw 3793  df-fin2 8158
 Copyright terms: Public domain W3C validator