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Theorem isnlly 20415
 Description: The property of being an n-locally topological space. (Contributed by Mario Carneiro, 2-Mar-2015.)
Assertion
Ref Expression
isnlly 𝑛Locally t
Distinct variable groups:   ,,,   ,,,

Proof of Theorem isnlly
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5881 . . . . . . 7
21fveq1d 5883 . . . . . 6
32ineq1d 3669 . . . . 5
4 oveq1 6312 . . . . . 6 t t
54eleq1d 2498 . . . . 5 t t
63, 5rexeqbidv 3047 . . . 4 t t
76ralbidv 2871 . . 3 t t
87raleqbi1dv 3040 . 2 t t
9 df-nlly 20413 . 2 𝑛Locally t
108, 9elrab2 3237 1 𝑛Locally t
 Colors of variables: wff setvar class Syntax hints:   wb 187   wa 370   wceq 1437   wcel 1870  wral 2782  wrex 2783   cin 3441  cpw 3985  csn 4002  cfv 5601  (class class class)co 6305   ↾t crest 15278  ctop 19848  cnei 20044  𝑛Locally cnlly 20411 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-or 371  df-an 372  df-3an 984  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-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-uni 4223  df-br 4427  df-iota 5565  df-fv 5609  df-ov 6308  df-nlly 20413 This theorem is referenced by:  nllytop  20419  nllyi  20421  llynlly  20423  nllyss  20426  nllyrest  20432  nllyidm  20435  hausllycmp  20440  cldllycmp  20441  txnlly  20583  cnllycmp  21880
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