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Theorem nllyss 17543
 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 3342 . . . . . . 7 t t
21reximdv 2817 . . . . . 6 t t
32ralimdv 2785 . . . . 5 t t
43ralimdv 2785 . . . 4 t t
54anim2d 549 . . 3 t t
6 isnlly 17532 . . 3 𝑛Locally t
7 isnlly 17532 . . 3 𝑛Locally t
85, 6, 73imtr4g 262 . 2 𝑛Locally 𝑛Locally
98ssrdv 3354 1 𝑛Locally 𝑛Locally
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1725  wral 2705  wrex 2706   cin 3319   wss 3320  cpw 3799  csn 3814  cfv 5454  (class class class)co 6081   ↾t crest 13648  ctop 16958  cnei 17161  𝑛Locally cnlly 17528 This theorem is referenced by:  iinllycon  24941  cvmlift3  25015 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084  df-nlly 17530
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