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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-omtrans2 | Unicode version |
Description: The set is transitive. (Contributed by BJ, 29-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-omtrans2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dftr3 4000 | . 2 | |
2 | bj-omtrans 13081 | . 2 | |
3 | 1, 2 | mprgbir 2467 | 1 |
Colors of variables: wff set class |
Syntax hints: wss 3041 wtr 3996 com 4474 |
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-in1 588 ax-in2 589 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-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-nul 4024 ax-pr 4101 ax-un 4325 ax-bd0 12938 ax-bdor 12941 ax-bdal 12943 ax-bdex 12944 ax-bdeq 12945 ax-bdel 12946 ax-bdsb 12947 ax-bdsep 13009 ax-infvn 13066 |
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-rex 2399 df-rab 2402 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-sn 3503 df-pr 3504 df-uni 3707 df-int 3742 df-tr 3997 df-suc 4263 df-iom 4475 df-bdc 12966 df-bj-ind 13052 |
This theorem is referenced by: bj-omord 13085 |
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