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Mirrors > Home > ILE Home > Th. List > addpiord | Unicode version |
Description: Positive integer addition in terms of ordinal addition. (Contributed by NM, 27-Aug-1995.) |
Ref | Expression |
---|---|
addpiord |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxpi 4541 | . 2 | |
2 | fvres 5413 | . . 3 | |
3 | df-ov 5745 | . . . 4 | |
4 | df-pli 7081 | . . . . 5 | |
5 | 4 | fveq1i 5390 | . . . 4 |
6 | 3, 5 | eqtri 2138 | . . 3 |
7 | df-ov 5745 | . . 3 | |
8 | 2, 6, 7 | 3eqtr4g 2175 | . 2 |
9 | 1, 8 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 cop 3500 cxp 4507 cres 4511 cfv 5093 (class class class)co 5742 coa 6278 cnpi 7048 cpli 7049 |
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-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 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-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-res 4521 df-iota 5058 df-fv 5101 df-ov 5745 df-pli 7081 |
This theorem is referenced by: addclpi 7103 addcompig 7105 addasspig 7106 distrpig 7109 addcanpig 7110 addnidpig 7112 ltexpi 7113 ltapig 7114 1lt2pi 7116 indpi 7118 archnqq 7193 prarloclemarch2 7195 nqnq0a 7230 |
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