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Mirrors > Home > ILE Home > Th. List > intunsn | Unicode version |
Description: Theorem joining a singleton to an intersection. (Contributed by NM, 29-Sep-2002.) |
Ref | Expression |
---|---|
intunsn.1 |
Ref | Expression |
---|---|
intunsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intun 3772 | . 2 | |
2 | intunsn.1 | . . . 4 | |
3 | 2 | intsn 3776 | . . 3 |
4 | 3 | ineq2i 3244 | . 2 |
5 | 1, 4 | eqtri 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wcel 1465 cvv 2660 cun 3039 cin 3040 csn 3497 cint 3741 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 df-un 3045 df-in 3047 df-sn 3503 df-pr 3504 df-int 3742 |
This theorem is referenced by: fiintim 6785 |
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