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Mirrors > Home > ILE Home > Th. List > cbvabw | Unicode version |
Description: Version of cbvab 2288 with a disjoint variable condition. (Contributed by Gino Giotto, 10-Jan-2024.) Reduce axiom usage. (Revised by Gino Giotto, 25-Aug-2024.) |
Ref | Expression |
---|---|
cbvabw.1 | |
cbvabw.2 | |
cbvabw.3 |
Ref | Expression |
---|---|
cbvabw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvabw.1 | . . . . . 6 | |
2 | 1 | nfsbv 1934 | . . . . 5 |
3 | equequ2 1700 | . . . . . . . 8 | |
4 | 3 | imbi1d 230 | . . . . . . 7 |
5 | 4 | albidv 1811 | . . . . . 6 |
6 | sb6 1873 | . . . . . 6 | |
7 | sb6 1873 | . . . . . 6 | |
8 | 5, 6, 7 | 3bitr4g 222 | . . . . 5 |
9 | 2, 8 | sbiev 1779 | . . . 4 |
10 | cbvabw.2 | . . . . . 6 | |
11 | cbvabw.3 | . . . . . 6 | |
12 | 10, 11 | sbiev 1779 | . . . . 5 |
13 | 12 | sbbii 1752 | . . . 4 |
14 | 9, 13 | bitr3i 185 | . . 3 |
15 | df-clab 2151 | . . 3 | |
16 | df-clab 2151 | . . 3 | |
17 | 14, 15, 16 | 3bitr4i 211 | . 2 |
18 | 17 | eqriv 2161 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 wceq 1342 wnf 1447 wsb 1749 wcel 2135 cab 2150 |
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-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 |
This theorem is referenced by: cbvsbcw 2973 |
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