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Theorem 1stctop 20389
 Description: A first-countable topology is a topology. (Contributed by Jeff Hankins, 22-Aug-2009.)
Assertion
Ref Expression
1stctop

Proof of Theorem 1stctop
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2429 . . 3
21is1stc 20387 . 2
32simplbi 461 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wcel 1870  wral 2782  wrex 2783   cin 3441  cpw 3985  cuni 4222   class class class wbr 4426  com 6706   cdom 7575  ctop 19848  c1stc 20383 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-in 3449  df-ss 3456  df-pw 3987  df-uni 4223  df-1stc 20385 This theorem is referenced by:  1stcfb  20391  1stcrest  20399  1stcelcls  20407  lly1stc  20442  1stckgen  20500  tx1stc  20596
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