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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 2697 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cvv 2686 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-v 2688 |
This theorem is referenced by: onunisuci 4354 ordsoexmid 4477 1oex 6321 fnoei 6348 oeiexg 6349 endisj 6718 unfiexmid 6806 snexxph 6838 djuex 6928 0ct 6992 infnninf 7022 nnnninf 7023 ctssexmid 7024 pm54.43 7046 prarloclemarch2 7227 opelreal 7635 elreal 7636 elreal2 7638 eqresr 7644 c0ex 7760 1ex 7761 pnfex 7819 sup3exmid 8715 2ex 8792 3ex 8796 elxr 9563 setsslid 12009 setsslnid 12010 subctctexmid 13196 0nninf 13197 nninfex 13205 nninffeq 13216 |
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