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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 3928 |
. 2
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2 | ax-14 1405 |
. . . . 5
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3 | 2 | alrimiv 1754 |
. . . 4
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4 | ax-13 1404 |
. . . 4
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5 | 3, 4 | embantd 50 |
. . 3
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6 | 5 | spimv 1692 |
. 2
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7 | 1, 6 | eximii 1493 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-pow 3927 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: dtruarb 3942 |
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