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Mirrors > Home > ILE Home > Th. List > csbopabg | Unicode version |
Description: Move substitution into a class abstraction. (Contributed by NM, 6-Aug-2007.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) |
Ref | Expression |
---|---|
csbopabg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 3010 |
. . 3
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2 | dfsbcq2 2916 |
. . . 4
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3 | 2 | opabbidv 4002 |
. . 3
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4 | 1, 3 | eqeq12d 2155 |
. 2
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5 | vex 2692 |
. . 3
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6 | nfs1v 1913 |
. . . 4
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7 | 6 | nfopab 4004 |
. . 3
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8 | sbequ12 1745 |
. . . 4
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9 | 8 | opabbidv 4002 |
. . 3
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10 | 5, 7, 9 | csbief 3049 |
. 2
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11 | 4, 10 | vtoclg 2749 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-sbc 2914 df-csb 3008 df-opab 3998 |
This theorem is referenced by: csbcnvg 4731 |
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