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Mirrors > Home > ILE Home > Th. List > mulpiord | Unicode version |
Description: Positive integer multiplication in terms of ordinal multiplication. (Contributed by NM, 27-Aug-1995.) |
Ref | Expression |
---|---|
mulpiord |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelxpi 4319 |
. 2
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2 | fvres 5141 |
. . 3
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3 | df-ov 5458 |
. . . 4
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4 | df-mi 6290 |
. . . . 5
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5 | 4 | fveq1i 5122 |
. . . 4
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6 | 3, 5 | eqtri 2057 |
. . 3
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7 | df-ov 5458 |
. . 3
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8 | 2, 6, 7 | 3eqtr4g 2094 |
. 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-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pow 3918 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-un 2916 df-in 2918 df-ss 2925 df-pw 3353 df-sn 3373 df-pr 3374 df-op 3376 df-uni 3572 df-br 3756 df-opab 3810 df-xp 4294 df-res 4300 df-iota 4810 df-fv 4853 df-ov 5458 df-mi 6290 |
This theorem is referenced by: mulidpi 6302 mulclpi 6312 mulcompig 6315 mulasspig 6316 distrpig 6317 mulcanpig 6319 ltmpig 6323 archnqq 6400 enq0enq 6414 addcmpblnq0 6426 mulcmpblnq0 6427 mulcanenq0ec 6428 addclnq0 6434 mulclnq0 6435 nqpnq0nq 6436 nqnq0a 6437 nqnq0m 6438 nq0m0r 6439 distrnq0 6442 addassnq0lemcl 6444 |
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