Theorem isfin2 8695

Description: Definition of a II-finite set. (Contributed by Stefan O'Rear, 16-May-2015.)

Assertion

Ref	Expression
isfin2

Distinct variable group:   ,

Proof of Theorem isfin2

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		pweq 4015	. . . 4
2	1	pweqd 4017	. . 3
3	2	raleqdv 3060	. 2
4		df-fin2 8687	. 2
5	3, 4	elab2g 3248	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  A.wral 2807  c0 3784  ~Pcpw 4012  U.cuni 4249  Orwor 4804  crpss 6579  cfin2 8680

This theorem is referenced by:  fin2i  8696  isfin2-2  8720  ssfin2  8721  enfin2i  8722  fin12  8814  fin1a2s  8815

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-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-in 3482  df-ss 3489  df-pw 4014  df-fin2 8687