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Theorem fingch 9013
 Description: A finite set is a GCH-set. (Contributed by Mario Carneiro, 15-May-2015.)
Assertion
Ref Expression
fingch GCH

Proof of Theorem fingch
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssun1 3672 . 2
2 df-gch 9011 . 2 GCH
31, 2sseqtr4i 3542 1 GCH
 Colors of variables: wff setvar class Syntax hints:   wn 3   wa 369  wal 1377  cab 2452   cun 3479   wss 3481  cpw 4016   class class class wbr 4453   csdm 7527  cfn 7528  GCHcgch 9010 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3120  df-un 3486  df-in 3488  df-ss 3495  df-gch 9011 This theorem is referenced by:  gch2  9065
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