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Mirrors > Home > ILE Home > Th. List > cbvcsbw | Unicode version |
Description: Version of cbvcsb 3054 with a disjoint variable condition. (Contributed by Gino Giotto, 10-Jan-2024.) |
Ref | Expression |
---|---|
cbvcsbw.1 | |
cbvcsbw.2 | |
cbvcsbw.3 |
Ref | Expression |
---|---|
cbvcsbw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvcsbw.1 | . . . . 5 | |
2 | 1 | nfcri 2306 | . . . 4 |
3 | cbvcsbw.2 | . . . . 5 | |
4 | 3 | nfcri 2306 | . . . 4 |
5 | cbvcsbw.3 | . . . . 5 | |
6 | 5 | eleq2d 2240 | . . . 4 |
7 | 2, 4, 6 | cbvsbcw 2982 | . . 3 |
8 | 7 | abbii 2286 | . 2 |
9 | df-csb 3050 | . 2 | |
10 | df-csb 3050 | . 2 | |
11 | 8, 9, 10 | 3eqtr4i 2201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 cab 2156 wnfc 2299 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-sbc 2956 df-csb 3050 |
This theorem is referenced by: cbvprod 11508 |
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