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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbccom 2956 | . . . 4 | |
2 | df-clab 2104 | . . . . 5 | |
3 | sbsbc 2886 | . . . . 5 | |
4 | 2, 3 | bitri 183 | . . . 4 |
5 | df-clab 2104 | . . . . . 6 | |
6 | sbsbc 2886 | . . . . . 6 | |
7 | 5, 6 | bitri 183 | . . . . 5 |
8 | 7 | sbcbii 2940 | . . . 4 |
9 | 1, 4, 8 | 3bitr4i 211 | . . 3 |
10 | sbcel2g 2994 | . . 3 | |
11 | 9, 10 | syl5rbb 192 | . 2 |
12 | 11 | eqrdv 2115 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 wsb 1720 cab 2103 wsbc 2882 csb 2975 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-sbc 2883 df-csb 2976 |
This theorem is referenced by: csbsng 3554 csbunig 3714 csbxpg 4590 csbdmg 4703 csbrng 4970 |
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