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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 3010 | . . 3 | |
2 | csbeq1 3010 | . . . 4 | |
3 | csbeq1 3010 | . . . 4 | |
4 | 2, 3 | ineq12d 3283 | . . 3 |
5 | 1, 4 | eqeq12d 2155 | . 2 |
6 | vex 2692 | . . 3 | |
7 | nfcsb1v 3040 | . . . 4 | |
8 | nfcsb1v 3040 | . . . 4 | |
9 | 7, 8 | nfin 3287 | . . 3 |
10 | csbeq1a 3016 | . . . 4 | |
11 | csbeq1a 3016 | . . . 4 | |
12 | 10, 11 | ineq12d 3283 | . . 3 |
13 | 6, 9, 12 | csbief 3049 | . 2 |
14 | 5, 13 | vtoclg 2749 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1332 wcel 1481 csb 3007 cin 3075 |
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-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rab 2426 df-v 2691 df-sbc 2914 df-csb 3008 df-in 3082 |
This theorem is referenced by: csbresg 4830 |
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