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Theorem fingch 8927
Description: A finite set is a GCH-set. (Contributed by Mario Carneiro, 15-May-2015.)
Assertion
Ref Expression
fingch

Proof of Theorem fingch
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssun1 3633 . 2
2 df-gch 8925 . 2
31, 2sseqtr4i 3503 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  /\wa 369  A.wal 1368  {cab 2439  u.cun 3440  C_wss 3442  ~Pcpw 3976   class class class wbr 4409   csdm 7443   cfn 7444   cgch 8924
This theorem is referenced by:  gch2  8979
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-v 3083  df-un 3447  df-in 3449  df-ss 3456  df-gch 8925
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