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Theorem ttukeylem2 8390
 Description: Lemma for ttukey 8398. 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 448 . . . . . 6
2 sspwb 4413 . . . . . 6
31, 2sylib 189 . . . . 5
4 ssrin 3566 . . . . 5
5 sstr2 3355 . . . . 5
63, 4, 53syl 19 . . . 4
7 ttukeylem.1 . . . . . 6
8 ttukeylem.2 . . . . . 6
9 ttukeylem.3 . . . . . 6
107, 8, 9ttukeylem1 8389 . . . . 5
1110adantr 452 . . . 4
127, 8, 9ttukeylem1 8389 . . . . 5
1312adantr 452 . . . 4
146, 11, 133imtr4d 260 . . 3
1514impancom 428 . 2
1615impr 603 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wcel 1725   cdif 3317   cin 3319   wss 3320  cpw 3799  cuni 4015  wf1o 5453  cfv 5454  cfn 7109  ccrd 7822 This theorem is referenced by:  ttukeylem6  8394  ttukeylem7  8395 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-rep 4320  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-reu 2712  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-pss 3336  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-tp 3822  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-tr 4303  df-eprel 4494  df-id 4498  df-po 4503  df-so 4504  df-fr 4541  df-we 4543  df-ord 4584  df-on 4585  df-lim 4586  df-suc 4587  df-om 4846  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-fv 5462  df-1o 6724  df-en 7110  df-dom 7111  df-fin 7113
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