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Theorem isnrm 17401
 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 5730 . . . . 5
21ineq1d 3543 . . . 4
3 fveq2 5730 . . . . . . . 8
43fveq1d 5732 . . . . . . 7
54sseq1d 3377 . . . . . 6
65anbi2d 686 . . . . 5
76rexeqbi1dv 2915 . . . 4
82, 7raleqbidv 2918 . . 3
98raleqbi1dv 2914 . 2
10 df-nrm 17383 . 2
119, 10elrab2 3096 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707  wrex 2708   cin 3321   wss 3322  cpw 3801  cfv 5456  ctop 16960  ccld 17082  ccl 17084  cnrm 17376 This theorem is referenced by:  nrmtop  17402  nrmsep3  17421  isnrm2  17424  kqnrmlem1  17777  kqnrmlem2  17778  nrmhmph  17828 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-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-nrm 17383
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