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Theorem nllyss 20495
 Description: The "n-locally" predicate respects inclusion. (Contributed by Mario Carneiro, 2-Mar-2015.)
Assertion
Ref Expression
nllyss 𝑛Locally 𝑛Locally

Proof of Theorem nllyss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssel 3426 . . . . . . 7 t t
21reximdv 2861 . . . . . 6 t t
32ralimdv 2798 . . . . 5 t t
43ralimdv 2798 . . . 4 t t
54anim2d 569 . . 3 t t
6 isnlly 20484 . . 3 𝑛Locally t
7 isnlly 20484 . . 3 𝑛Locally t
85, 6, 73imtr4g 274 . 2 𝑛Locally 𝑛Locally
98ssrdv 3438 1 𝑛Locally 𝑛Locally
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   wcel 1887  wral 2737  wrex 2738   cin 3403   wss 3404  cpw 3951  csn 3968  cfv 5582  (class class class)co 6290   ↾t crest 15319  ctop 19917  cnei 20113  𝑛Locally cnlly 20480 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rex 2743  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-uni 4199  df-br 4403  df-iota 5546  df-fv 5590  df-ov 6293  df-nlly 20482 This theorem is referenced by:  iinllycon  29977  cvmlift3  30051
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