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Theorem ttukeylem2 8907
 Description: Lemma for ttukey 8915. A property of finite character is closed under subsets. (Contributed by Mario Carneiro, 15-May-2015.)
Hypotheses
Ref Expression
ttukeylem.1
ttukeylem.2
ttukeylem.3
Assertion
Ref Expression
ttukeylem2
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ttukeylem2
StepHypRef Expression
1 simpr 461 . . . . . 6
2 sspwb 4705 . . . . . 6
31, 2sylib 196 . . . . 5
4 ssrin 3719 . . . . 5
5 sstr2 3506 . . . . 5
63, 4, 53syl 20 . . . 4
7 ttukeylem.1 . . . . . 6
8 ttukeylem.2 . . . . . 6
9 ttukeylem.3 . . . . . 6
107, 8, 9ttukeylem1 8906 . . . . 5
1110adantr 465 . . . 4
127, 8, 9ttukeylem1 8906 . . . . 5
1312adantr 465 . . . 4
146, 11, 133imtr4d 268 . . 3
1514impancom 440 . 2
1615impr 619 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1393   wcel 1819   cdif 3468   cin 3470   wss 3471  cpw 4015  cuni 4251  wf1o 5593  cfv 5594  cfn 7535  ccrd 8333 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-8 1821  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-rep 4568  ax-sep 4578  ax-nul 4586  ax-pow 4634  ax-pr 4695  ax-un 6591 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-reu 2814  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3431  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-pss 3487  df-nul 3794  df-if 3945  df-pw 4017  df-sn 4033  df-pr 4035  df-tp 4037  df-op 4039  df-uni 4252  df-iun 4334  df-br 4457  df-opab 4516  df-mpt 4517  df-tr 4551  df-eprel 4800  df-id 4804  df-po 4809  df-so 4810  df-fr 4847  df-we 4849  df-ord 4890  df-on 4891  df-lim 4892  df-suc 4893  df-xp 5014  df-rel 5015  df-cnv 5016  df-co 5017  df-dm 5018  df-rn 5019  df-res 5020  df-ima 5021  df-iota 5557  df-fun 5596  df-fn 5597  df-f 5598  df-f1 5599  df-fo 5600  df-f1o 5601  df-fv 5602  df-om 6700  df-1o 7148  df-en 7536  df-dom 7537  df-fin 7539 This theorem is referenced by:  ttukeylem6  8911  ttukeylem7  8912
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