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Mirrors > Home > ILE Home > Th. List > el | Unicode version |
Description: Every set is an element of some other set. (Contributed by NM, 4-Jan-2002.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
el |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zfpow 4107 |
. 2
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2 | ax-14 1493 |
. . . . 5
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3 | 2 | alrimiv 1847 |
. . . 4
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4 | ax-13 1492 |
. . . 4
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5 | 3, 4 | embantd 56 |
. . 3
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6 | 5 | spimv 1784 |
. 2
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7 | 1, 6 | eximii 1582 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-pow 4106 |
This theorem depends on definitions: df-bi 116 df-nf 1438 |
This theorem is referenced by: dtruarb 4123 |
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