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Mirrors > Home > ILE Home > Th. List > elexi | Unicode version |
Description: If a class is a member of another class, it is a set. (Contributed by NM, 11-Jun-1994.) |
Ref | Expression |
---|---|
elisseti.1 |
Ref | Expression |
---|---|
elexi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisseti.1 | . 2 | |
2 | elex 2671 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 cvv 2660 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-v 2662 |
This theorem is referenced by: onunisuci 4324 ordsoexmid 4447 1oex 6289 fnoei 6316 oeiexg 6317 endisj 6686 unfiexmid 6774 snexxph 6806 djuex 6896 0ct 6960 infnninf 6990 nnnninf 6991 ctssexmid 6992 pm54.43 7014 prarloclemarch2 7195 opelreal 7603 elreal 7604 elreal2 7606 eqresr 7612 c0ex 7728 1ex 7729 pnfex 7787 sup3exmid 8683 2ex 8760 3ex 8764 elxr 9531 setsslid 11936 setsslnid 11937 subctctexmid 13123 0nninf 13124 nninfex 13132 nninffeq 13143 |
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