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Theorem llyssnlly 22058
Description: A locally 𝐴 space is n-locally 𝐴. (Contributed by Mario Carneiro, 2-Mar-2015.)
Assertion
Ref Expression
llyssnlly Locally 𝐴 ⊆ 𝑛-Locally 𝐴

Proof of Theorem llyssnlly
Dummy variable 𝑗 is distinct from all other variables.
StepHypRef Expression
1 llynlly 22057 . 2 (𝑗 ∈ Locally 𝐴𝑗 ∈ 𝑛-Locally 𝐴)
21ssriv 3946 1 Locally 𝐴 ⊆ 𝑛-Locally 𝐴
Colors of variables: wff setvar class
Syntax hints:  wss 3909  Locally clly 22044  𝑛-Locally cnlly 22045
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2792  ax-rep 5162  ax-sep 5175  ax-nul 5182  ax-pow 5238  ax-pr 5302
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-mo 2622  df-eu 2653  df-clab 2799  df-cleq 2813  df-clel 2891  df-nfc 2959  df-ne 3007  df-ral 3130  df-rex 3131  df-reu 3132  df-rab 3134  df-v 3472  df-sbc 3749  df-csb 3857  df-dif 3912  df-un 3914  df-in 3916  df-ss 3926  df-nul 4266  df-if 4440  df-pw 4513  df-sn 4540  df-pr 4542  df-op 4546  df-uni 4811  df-iun 4893  df-br 5039  df-opab 5101  df-mpt 5119  df-id 5432  df-xp 5533  df-rel 5534  df-cnv 5535  df-co 5536  df-dm 5537  df-rn 5538  df-res 5539  df-ima 5540  df-iota 6286  df-fun 6329  df-fn 6330  df-f 6331  df-f1 6332  df-fo 6333  df-f1o 6334  df-fv 6335  df-ov 7132  df-top 21474  df-nei 21678  df-lly 22046  df-nlly 22047
This theorem is referenced by:  restnlly  22062  iinllyconn  32505
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