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Theorem llyss 17543
 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 3343 . . . . . . . 8 t t
21anim2d 550 . . . . . . 7 t t
32reximdv 2818 . . . . . 6 t t
43ralimdv 2786 . . . . 5 t t
54ralimdv 2786 . . . 4 t t
65anim2d 550 . . 3 t t
7 islly 17532 . . 3 Locally t
8 islly 17532 . . 3 Locally t
96, 7, 83imtr4g 263 . 2 Locally Locally
109ssrdv 3355 1 Locally Locally
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wcel 1726  wral 2706  wrex 2707   cin 3320   wss 3321  cpw 3800  (class class class)co 6082   ↾t crest 13649  ctop 16959  Locally clly 17528 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-iota 5419  df-fv 5463  df-ov 6085  df-lly 17530
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