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Mirrors > Home > ILE Home > Th. List > tron | Unicode version |
Description: The class of all ordinal numbers is transitive. (Contributed by NM, 4-May-2009.) |
Ref | Expression |
---|---|
tron |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dftr3 4078 | . 2 | |
2 | vex 2724 | . . . . . . 7 | |
3 | 2 | elon 4346 | . . . . . 6 |
4 | ordelord 4353 | . . . . . 6 | |
5 | 3, 4 | sylanb 282 | . . . . 5 |
6 | 5 | ex 114 | . . . 4 |
7 | vex 2724 | . . . . 5 | |
8 | 7 | elon 4346 | . . . 4 |
9 | 6, 8 | syl6ibr 161 | . . 3 |
10 | 9 | ssrdv 3143 | . 2 |
11 | 1, 10 | mprgbir 2522 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2135 wss 3111 wtr 4074 word 4334 con0 4335 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-in 3117 df-ss 3124 df-uni 3784 df-tr 4075 df-iord 4338 df-on 4340 |
This theorem is referenced by: ordon 4457 tfi 4553 |
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