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Mirrors > Home > ILE Home > Th. List > disjssun | Unicode version |
Description: Subset relation for disjoint classes. (Contributed by NM, 25-Oct-2005.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
disjssun |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | indi 3396 |
. . . . 5
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2 | 1 | equncomi 3295 |
. . . 4
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3 | uneq2 3297 |
. . . . 5
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4 | un0 3470 |
. . . . 5
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5 | 3, 4 | eqtrdi 2237 |
. . . 4
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6 | 2, 5 | eqtrid 2233 |
. . 3
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7 | 6 | eqeq1d 2197 |
. 2
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8 | df-ss 3156 |
. 2
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9 | df-ss 3156 |
. 2
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10 | 7, 8, 9 | 3bitr4g 223 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2170 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-v 2753 df-dif 3145 df-un 3147 df-in 3149 df-ss 3156 df-nul 3437 |
This theorem is referenced by: (None) |
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