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Mirrors > Home > ILE Home > Th. List > elex2 | Unicode version |
Description: If a class contains another class, then it contains some set. (Contributed by Alan Sare, 25-Sep-2011.) |
Ref | Expression |
---|---|
elex2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1a 2249 |
. . 3
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2 | 1 | alrimiv 1874 |
. 2
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3 | elisset 2751 |
. 2
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4 | exim 1599 |
. 2
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5 | 2, 3, 4 | sylc 62 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-v 2739 |
This theorem is referenced by: snmg 3710 oprcl 3802 brm 4053 ss1o0el1 4197 exss 4227 onintrab2im 4517 regexmidlemm 4531 dmxpid 4848 acexmidlem2 5871 frecabcl 6399 ixpm 6729 enm 6819 ssfilem 6874 fin0 6884 fin0or 6885 diffitest 6886 diffisn 6892 infm 6903 inffiexmid 6905 ctssdc 7111 omct 7115 ctssexmid 7147 exmidfodomrlemr 7200 exmidfodomrlemrALT 7201 exmidaclem 7206 caucvgsrlemasr 7788 suplocsrlempr 7805 gtso 8035 sup3exmid 8913 indstr 9592 negm 9614 fzm 10037 fzom 10163 rexfiuz 10997 r19.2uz 11001 resqrexlemgt0 11028 climuni 11300 bezoutlembi 12005 lcmgcdlem 12076 pcprecl 12288 pc2dvds 12328 nninfdclemcl 12448 dfgrp3m 12968 issubg2m 13047 issubgrpd2 13048 issubg3 13050 issubg4m 13051 grpissubg 13052 subgintm 13056 nmzsubg 13068 dvdsr02 13272 01eq0ring 13328 subrgugrp 13359 cnsubglem 13443 tgioo 14016 pw1nct 14722 nninfall 14728 |
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