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Theorem gchen2 9025
Description: If A ~PA, and is an infinite GCH-set, then in cardinality. (Contributed by Mario Carneiro, 15-May-2015.)
Assertion
Ref Expression
gchen2

Proof of Theorem gchen2
StepHypRef Expression
1 simprr 757 . 2
2 gchi 9023 . . . . . 6
323expia 1198 . . . . 5
43con3dimp 441 . . . 4
54an32s 804 . . 3
65adantrr 716 . 2
7 bren2 7566 . 2
81, 6, 7sylanbrc 664 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  e.wcel 1818  ~Pcpw 4012   class class class wbr 4452   cen 7533   cdom 7534   csdm 7535   cfn 7536   cgch 9019
This theorem is referenced by:  gchhar  9078
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-pw 4014  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-f1o 5600  df-en 7537  df-dom 7538  df-sdom 7539  df-gch 9020
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