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Mirrors > Home > ILE Home > Th. List > csbing | Unicode version |
Description: Distribute proper substitution through an intersection relation. (Contributed by Alan Sare, 22-Jul-2012.) |
Ref | Expression |
---|---|
csbing |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 3052 | . . 3 | |
2 | csbeq1 3052 | . . . 4 | |
3 | csbeq1 3052 | . . . 4 | |
4 | 2, 3 | ineq12d 3329 | . . 3 |
5 | 1, 4 | eqeq12d 2185 | . 2 |
6 | vex 2733 | . . 3 | |
7 | nfcsb1v 3082 | . . . 4 | |
8 | nfcsb1v 3082 | . . . 4 | |
9 | 7, 8 | nfin 3333 | . . 3 |
10 | csbeq1a 3058 | . . . 4 | |
11 | csbeq1a 3058 | . . . 4 | |
12 | 10, 11 | ineq12d 3329 | . . 3 |
13 | 6, 9, 12 | csbief 3093 | . 2 |
14 | 5, 13 | vtoclg 2790 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 csb 3049 cin 3120 |
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-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rab 2457 df-v 2732 df-sbc 2956 df-csb 3050 df-in 3127 |
This theorem is referenced by: csbresg 4892 |
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