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Theorem t0dist 17391
 Description: Any two distinct points in a T0 space are topologically distinguishable. (Contributed by Jeff Hankins, 1-Feb-2010.)
Hypothesis
Ref Expression
ist0.1
Assertion
Ref Expression
t0dist
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem t0dist
StepHypRef Expression
1 ist0.1 . . . . . 6
21t0sep 17390 . . . . 5
32necon3ad 2639 . . . 4
43exp32 590 . . 3
543imp2 1169 . 2
6 rexnal 2718 . 2
75, 6sylibr 205 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360   w3a 937   wceq 1653   wcel 1726   wne 2601  wral 2707  wrex 2708  cuni 4017  ct0 17372 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-uni 4018  df-t0 17379
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