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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 2988 | . . . 4 | |
2 | df-clab 2127 | . . . . 5 | |
3 | sbsbc 2917 | . . . . 5 | |
4 | 2, 3 | bitri 183 | . . . 4 |
5 | df-clab 2127 | . . . . . 6 | |
6 | sbsbc 2917 | . . . . . 6 | |
7 | 5, 6 | bitri 183 | . . . . 5 |
8 | 7 | sbcbii 2972 | . . . 4 |
9 | 1, 4, 8 | 3bitr4i 211 | . . 3 |
10 | sbcel2g 3028 | . . 3 | |
11 | 9, 10 | syl5rbb 192 | . 2 |
12 | 11 | eqrdv 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1332 wcel 1481 wsb 1736 cab 2126 wsbc 2913 csb 3007 |
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-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 |
This theorem is referenced by: csbsng 3592 csbunig 3752 csbxpg 4628 csbdmg 4741 csbrng 5008 |
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