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Mirrors > Home > ILE Home > Th. List > csbunig | Unicode version |
Description: Distribute proper substitution through the union of a class. (Contributed by Alan Sare, 10-Nov-2012.) |
Ref | Expression |
---|---|
csbunig |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbabg 2990 |
. . 3
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2 | sbcexg 2894 |
. . . . 5
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3 | sbcang 2883 |
. . . . . . 7
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4 | sbcg 2909 |
. . . . . . . 8
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5 | sbcel2g 2953 |
. . . . . . . 8
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6 | 4, 5 | anbi12d 458 |
. . . . . . 7
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7 | 3, 6 | bitrd 187 |
. . . . . 6
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8 | 7 | exbidv 1754 |
. . . . 5
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9 | 2, 8 | bitrd 187 |
. . . 4
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10 | 9 | abbidv 2206 |
. . 3
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11 | 1, 10 | eqtrd 2121 |
. 2
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12 | df-uni 3660 |
. . 3
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13 | 12 | csbeq2i 2958 |
. 2
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14 | df-uni 3660 |
. 2
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15 | 11, 13, 14 | 3eqtr4g 2146 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2622 df-sbc 2842 df-csb 2935 df-uni 3660 |
This theorem is referenced by: (None) |
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