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Mirrors > Home > ILE Home > Th. List > 9t11e99 | Unicode version |
Description: 9 times 11 equals 99. (Contributed by AV, 14-Jun-2021.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
9t11e99 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9cn 8666 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | 10nn0 9051 |
. . . . . 6
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3 | 2 | nn0cni 8841 |
. . . . 5
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4 | ax-1cn 7588 |
. . . . 5
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5 | 3, 4 | mulcli 7643 |
. . . 4
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6 | 1, 5, 4 | adddii 7648 |
. . 3
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7 | 3 | mulid1i 7640 |
. . . . . 6
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8 | 7 | oveq2i 5717 |
. . . . 5
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9 | 1, 3 | mulcomi 7644 |
. . . . 5
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10 | 8, 9 | eqtri 2120 |
. . . 4
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11 | 1 | mulid1i 7640 |
. . . 4
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12 | 10, 11 | oveq12i 5718 |
. . 3
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13 | 6, 12 | eqtri 2120 |
. 2
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14 | dfdec10 9037 |
. . 3
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15 | 14 | oveq2i 5717 |
. 2
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16 | dfdec10 9037 |
. 2
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17 | 13, 15, 16 | 3eqtr4i 2130 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-pr 4069 ax-setind 4390 ax-cnex 7586 ax-resscn 7587 ax-1cn 7588 ax-1re 7589 ax-icn 7590 ax-addcl 7591 ax-addrcl 7592 ax-mulcl 7593 ax-addcom 7595 ax-mulcom 7596 ax-addass 7597 ax-mulass 7598 ax-distr 7599 ax-i2m1 7600 ax-1rid 7602 ax-0id 7603 ax-rnegex 7604 ax-cnre 7606 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-eu 1963 df-mo 1964 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ne 2268 df-ral 2380 df-rex 2381 df-reu 2382 df-rab 2384 df-v 2643 df-sbc 2863 df-dif 3023 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-int 3719 df-br 3876 df-opab 3930 df-id 4153 df-xp 4483 df-rel 4484 df-cnv 4485 df-co 4486 df-dm 4487 df-iota 5024 df-fun 5061 df-fv 5067 df-riota 5662 df-ov 5709 df-oprab 5710 df-mpo 5711 df-sub 7806 df-inn 8579 df-2 8637 df-3 8638 df-4 8639 df-5 8640 df-6 8641 df-7 8642 df-8 8643 df-9 8644 df-n0 8830 df-dec 9035 |
This theorem is referenced by: 3dvds2dec 11358 |
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