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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxpi 4654 |
. 2
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2 | fvres 5534 |
. . 3
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3 | df-ov 5871 |
. . . 4
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4 | df-pli 7282 |
. . . . 5
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5 | 4 | fveq1i 5511 |
. . . 4
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6 | 3, 5 | eqtri 2198 |
. . 3
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7 | df-ov 5871 |
. . 3
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8 | 2, 6, 7 | 3eqtr4g 2235 |
. 2
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9 | 1, 8 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-xp 4628 df-res 4634 df-iota 5173 df-fv 5219 df-ov 5871 df-pli 7282 |
This theorem is referenced by: addclpi 7304 addcompig 7306 addasspig 7307 distrpig 7310 addcanpig 7311 addnidpig 7313 ltexpi 7314 ltapig 7315 1lt2pi 7317 indpi 7319 archnqq 7394 prarloclemarch2 7396 nqnq0a 7431 |
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