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Theorem llyss 20486
 Description: The "locally" predicate respects inclusion. (Contributed by Mario Carneiro, 2-Mar-2015.)
Assertion
Ref Expression
llyss Locally Locally

Proof of Theorem llyss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssel 3459 . . . . . . . 8 t t
21anim2d 568 . . . . . . 7 t t
32reximdv 2900 . . . . . 6 t t
43ralimdv 2836 . . . . 5 t t
54ralimdv 2836 . . . 4 t t
65anim2d 568 . . 3 t t
7 islly 20475 . . 3 Locally t
8 islly 20475 . . 3 Locally t
96, 7, 83imtr4g 274 . 2 Locally Locally
109ssrdv 3471 1 Locally Locally
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   wcel 1869  wral 2776  wrex 2777   cin 3436   wss 3437  cpw 3980  (class class class)co 6303   ↾t crest 15312  ctop 19909  Locally clly 20471 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 985  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ral 2781  df-rex 2782  df-rab 2785  df-v 3084  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3763  df-if 3911  df-sn 3998  df-pr 4000  df-op 4004  df-uni 4218  df-br 4422  df-iota 5563  df-fv 5607  df-ov 6306  df-lly 20473 This theorem is referenced by: (None)
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