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Mirrors > Home > ILE Home > Th. List > csbabg | Unicode version |
Description: Move substitution into a class abstraction. (Contributed by NM, 13-Dec-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
csbabg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbccom 2833 |
. . . 4
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2 | df-clab 2027 |
. . . . 5
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3 | sbsbc 2768 |
. . . . 5
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4 | 2, 3 | bitri 173 |
. . . 4
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5 | df-clab 2027 |
. . . . . 6
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6 | sbsbc 2768 |
. . . . . 6
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7 | 5, 6 | bitri 173 |
. . . . 5
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8 | 7 | sbcbii 2818 |
. . . 4
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9 | 1, 4, 8 | 3bitr4i 201 |
. . 3
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10 | sbcel2g 2871 |
. . 3
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11 | 9, 10 | syl5rbb 182 |
. 2
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12 | 11 | eqrdv 2038 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sbc 2765 df-csb 2853 |
This theorem is referenced by: csbsng 3431 csbunig 3588 csbxpg 4421 csbdmg 4529 csbrng 4782 |
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