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Mirrors > Home > ILE Home > Th. List > csbvarg | Unicode version |
Description: The proper substitution of a class for setvar variable results in the class (if the class exists). (Contributed by NM, 10-Nov-2005.) |
Ref | Expression |
---|---|
csbvarg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2630 |
. 2
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2 | vex 2622 |
. . . . . 6
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3 | df-csb 2934 |
. . . . . . 7
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4 | sbcel2gv 2902 |
. . . . . . . 8
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5 | 4 | abbi1dv 2207 |
. . . . . . 7
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6 | 3, 5 | syl5eq 2132 |
. . . . . 6
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7 | 2, 6 | ax-mp 7 |
. . . . 5
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8 | 7 | csbeq2i 2957 |
. . . 4
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9 | csbco 2942 |
. . . 4
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10 | df-csb 2934 |
. . . 4
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11 | 8, 9, 10 | 3eqtr3i 2116 |
. . 3
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12 | sbcel2gv 2902 |
. . . 4
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13 | 12 | abbi1dv 2207 |
. . 3
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14 | 11, 13 | syl5eq 2132 |
. 2
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15 | 1, 14 | syl 14 |
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 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-sbc 2841 df-csb 2934 |
This theorem is referenced by: sbccsb2g 2960 csbfvg 5342 f1od2 6000 bj-sels 11805 |
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