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Theorem isnrm 20127
 Description: The predicate "is a normal space." Much like the case for regular spaces, normal does not imply Hausdorff or even regular. (Contributed by Jeff Hankins, 1-Feb-2010.) (Revised by Mario Carneiro, 24-Aug-2015.)
Assertion
Ref Expression
isnrm
Distinct variable group:   ,,,

Proof of Theorem isnrm
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5848 . . . . 5
21ineq1d 3639 . . . 4
3 fveq2 5848 . . . . . . . 8
43fveq1d 5850 . . . . . . 7
54sseq1d 3468 . . . . . 6
65anbi2d 702 . . . . 5
76rexeqbi1dv 3012 . . . 4
82, 7raleqbidv 3017 . . 3
98raleqbi1dv 3011 . 2
10 df-nrm 20109 . 2
119, 10elrab2 3208 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 367   wceq 1405   wcel 1842  wral 2753  wrex 2754   cin 3412   wss 3413  cpw 3954  cfv 5568  ctop 19684  ccld 19807  ccl 19809  cnrm 20102 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2758  df-rex 2759  df-rab 2762  df-v 3060  df-dif 3416  df-un 3418  df-in 3420  df-ss 3427  df-nul 3738  df-if 3885  df-sn 3972  df-pr 3974  df-op 3978  df-uni 4191  df-br 4395  df-iota 5532  df-fv 5576  df-nrm 20109 This theorem is referenced by:  nrmtop  20128  nrmsep3  20147  isnrm2  20150  kqnrmlem1  20534  kqnrmlem2  20535  nrmhmph  20585
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