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Theorem llyi 17529
 Description: The property of a locally topological space. (Contributed by Mario Carneiro, 2-Mar-2015.)
Assertion
Ref Expression
llyi Locally t
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem llyi
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 islly 17523 . . . . 5 Locally t
21simprbi 451 . . . 4 Locally t
3 pweq 3794 . . . . . . . 8
43ineq2d 3534 . . . . . . 7
54rexeqdv 2903 . . . . . 6 t t
65raleqbi1dv 2904 . . . . 5 t t
76rspccva 3043 . . . 4 t t
82, 7sylan 458 . . 3 Locally t
9 eleq1 2495 . . . . . . . 8
109anbi1d 686 . . . . . . 7 t t
1110anbi2d 685 . . . . . 6 t t
12 anass 631 . . . . . . 7 t t
13 elin 3522 . . . . . . . . 9
14 vex 2951 . . . . . . . . . . 11
1514elpw 3797 . . . . . . . . . 10
1615anbi2i 676 . . . . . . . . 9
1713, 16bitri 241 . . . . . . . 8
1817anbi1i 677 . . . . . . 7 t t
19 3anass 940 . . . . . . . 8 t t
2019anbi2i 676 . . . . . . 7 t t
2112, 18, 203bitr4i 269 . . . . . 6 t t
2211, 21syl6bb 253 . . . . 5 t t
2322rexbidv2 2720 . . . 4 t t
2423rspccva 3043 . . 3 t t
258, 24sylan 458 . 2 Locally t
26253impa 1148 1 Locally t
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   w3a 936   wceq 1652   wcel 1725  wral 2697  wrex 2698   cin 3311   wss 3312  cpw 3791  (class class class)co 6073   ↾t crest 13640  ctop 16950  Locally clly 17519 This theorem is referenced by:  llynlly  17532  islly2  17539  llyrest  17540  llyidm  17543  nllyidm  17544  lly1stc  17551  dislly  17552  txlly  17660  cvmlift2lem10  24991 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076  df-lly 17521
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