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Theorem islly 19775
 Description: The property of being a locally topological space. (Contributed by Mario Carneiro, 2-Mar-2015.)
Assertion
Ref Expression
islly Locally t
Distinct variable groups:   ,,,   ,,,

Proof of Theorem islly
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ineq1 3693 . . . . 5
2 oveq1 6292 . . . . . . 7 t t
32eleq1d 2536 . . . . . 6 t t
43anbi2d 703 . . . . 5 t t
51, 4rexeqbidv 3073 . . . 4 t t
65ralbidv 2903 . . 3 t t
76raleqbi1dv 3066 . 2 t t
8 df-lly 19773 . 2 Locally t
97, 8elrab2 3263 1 Locally t
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1379   wcel 1767  wral 2814  wrex 2815   cin 3475  cpw 4010  (class class class)co 6285   ↾t crest 14679  ctop 19201  Locally clly 19771 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-br 4448  df-iota 5551  df-fv 5596  df-ov 6288  df-lly 19773 This theorem is referenced by:  llytop  19779  llyi  19781  llyss  19786  subislly  19788  restnlly  19789  restlly  19790  islly2  19791  llyrest  19792  llyidm  19795  dislly  19804  txlly  19964  ismntop  27755  cnllyscon  28441  rellyscon  28447
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