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Mirrors > Home > ILE Home > Th. List > sess1 | Unicode version |
Description: Subset theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.) |
Ref | Expression |
---|---|
sess1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 107 |
. . . . . 6
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2 | 1 | ssbrd 3855 |
. . . . 5
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3 | 2 | ss2rabdv 3088 |
. . . 4
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4 | ssexg 3946 |
. . . . 5
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5 | 4 | ex 113 |
. . . 4
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6 | 3, 5 | syl 14 |
. . 3
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7 | 6 | ralimdv 2438 |
. 2
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8 | df-se 4127 |
. 2
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9 | df-se 4127 |
. 2
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10 | 7, 8, 9 | 3imtr4g 203 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 ax-sep 3925 |
This theorem depends on definitions: df-bi 115 df-tru 1290 df-nf 1393 df-sb 1690 df-clab 2072 df-cleq 2078 df-clel 2081 df-nfc 2214 df-ral 2360 df-rab 2364 df-v 2616 df-in 2992 df-ss 2999 df-br 3815 df-se 4127 |
This theorem is referenced by: seeq1 4133 |
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