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Theorem topontopi 16996
Description: A topology on a given base set is a topology. (Contributed by Mario Carneiro, 13-Aug-2015.)
Hypothesis
Ref Expression
topontopi.1  |-  J  e.  (TopOn `  B )
Assertion
Ref Expression
topontopi  |-  J  e. 
Top

Proof of Theorem topontopi
StepHypRef Expression
1 topontopi.1 . 2  |-  J  e.  (TopOn `  B )
2 topontop 16991 . 2  |-  ( J  e.  (TopOn `  B
)  ->  J  e.  Top )
31, 2ax-mp 8 1  |-  J  e. 
Top
Colors of variables: wff set class
Syntax hints:    e. wcel 1725   ` cfv 5454   Topctop 16958  TopOnctopon 16959
This theorem is referenced by:  sn0top  17063  indistop  17066  letop  17270  dfac14  17650  cnfldtop  18818  sszcld  18848  iitop  18910  limccnp2  19779  cxpcn3  20632  lmlim  24333  pnfneige0  24336  sxbrsigalem4  24637
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-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-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-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-iota 5418  df-fun 5456  df-fv 5462  df-topon 16966
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