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Theorem inttop3 25516
 Description: The intersection of a family of topologies is a topology. (Contributed by FL, 19-Sep-2011.)
Assertion
Ref Expression
inttop3

Proof of Theorem inttop3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 intiin 3956 . 2
2 dfss3 3170 . . 3
3 inttop2 25515 . . 3
42, 3sylan2b 461 . 2
51, 4syl5eqel 2367 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wcel 1684   wne 2446  wral 2543   wss 3152  c0 3455  cint 3862  ciin 3906  ctop 16631 This theorem is referenced by:  inttop4  25517  prtoptop  25549 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-un 4512 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166  df-nul 3456  df-pw 3627  df-uni 3828  df-int 3863  df-iin 3908  df-top 16636
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