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Mirrors > Home > ILE Home > Th. List > csbov123g | Unicode version |
Description: Move class substitution in and out of an operation. (Contributed by NM, 12-Nov-2005.) (Proof shortened by Mario Carneiro, 5-Dec-2016.) |
Ref | Expression |
---|---|
csbov123g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 2937 |
. . 3
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2 | csbeq1 2937 |
. . . 4
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3 | csbeq1 2937 |
. . . 4
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4 | csbeq1 2937 |
. . . 4
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5 | 2, 3, 4 | oveq123d 5687 |
. . 3
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6 | 1, 5 | eqeq12d 2103 |
. 2
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7 | vex 2623 |
. . 3
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8 | nfcsb1v 2964 |
. . . 4
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9 | nfcsb1v 2964 |
. . . 4
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10 | nfcsb1v 2964 |
. . . 4
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11 | 8, 9, 10 | nfov 5693 |
. . 3
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12 | csbeq1a 2942 |
. . . 4
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13 | csbeq1a 2942 |
. . . 4
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14 | csbeq1a 2942 |
. . . 4
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15 | 12, 13, 14 | oveq123d 5687 |
. . 3
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16 | 7, 11, 15 | csbief 2973 |
. 2
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17 | 6, 16 | vtoclg 2680 |
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-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rex 2366 df-v 2622 df-sbc 2842 df-csb 2935 df-un 3004 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-iota 4993 df-fv 5036 df-ov 5669 |
This theorem is referenced by: csbov12g 5702 |
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