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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 3030 | . . . 4 | |
2 | df-clab 2157 | . . . . 5 | |
3 | sbsbc 2959 | . . . . 5 | |
4 | 2, 3 | bitri 183 | . . . 4 |
5 | df-clab 2157 | . . . . . 6 | |
6 | sbsbc 2959 | . . . . . 6 | |
7 | 5, 6 | bitri 183 | . . . . 5 |
8 | 7 | sbcbii 3014 | . . . 4 |
9 | 1, 4, 8 | 3bitr4i 211 | . . 3 |
10 | sbcel2g 3070 | . . 3 | |
11 | 9, 10 | bitr2id 192 | . 2 |
12 | 11 | eqrdv 2168 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wsb 1755 wcel 2141 cab 2156 wsbc 2955 csb 3049 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-sbc 2956 df-csb 3050 |
This theorem is referenced by: csbsng 3642 csbunig 3802 csbxpg 4690 csbdmg 4803 csbrng 5070 |
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