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Mirrors > Home > ILE Home > Th. List > 9t7e63 | Unicode version |
Description: 9 times 7 equals 63. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
9t7e63 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9nn0 9196 |
. 2
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2 | 6nn0 9193 |
. 2
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3 | df-7 8979 |
. 2
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4 | 9t6e54 9505 |
. 2
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5 | 5nn0 9192 |
. . 3
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6 | 4nn0 9191 |
. . 3
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7 | eqid 2177 |
. . 3
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8 | 5p1e6 9052 |
. . 3
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9 | 3nn0 9190 |
. . 3
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10 | 1 | nn0cni 9184 |
. . . 4
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11 | 6 | nn0cni 9184 |
. . . 4
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12 | 9p4e13 9468 |
. . . 4
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13 | 10, 11, 12 | addcomli 8098 |
. . 3
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14 | 5, 6, 1, 7, 8, 9, 13 | decaddci 9440 |
. 2
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15 | 1, 2, 3, 4, 14 | 4t3lem 9476 |
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-in1 614 ax-in2 615 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 4120 ax-pow 4173 ax-pr 4208 ax-setind 4535 ax-cnex 7899 ax-resscn 7900 ax-1cn 7901 ax-1re 7902 ax-icn 7903 ax-addcl 7904 ax-addrcl 7905 ax-mulcl 7906 ax-addcom 7908 ax-mulcom 7909 ax-addass 7910 ax-mulass 7911 ax-distr 7912 ax-i2m1 7913 ax-1rid 7915 ax-0id 7916 ax-rnegex 7917 ax-cnre 7919 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4003 df-opab 4064 df-id 4292 df-xp 4631 df-rel 4632 df-cnv 4633 df-co 4634 df-dm 4635 df-iota 5177 df-fun 5217 df-fv 5223 df-riota 5828 df-ov 5875 df-oprab 5876 df-mpo 5877 df-sub 8126 df-inn 8916 df-2 8974 df-3 8975 df-4 8976 df-5 8977 df-6 8978 df-7 8979 df-8 8980 df-9 8981 df-n0 9173 df-dec 9381 |
This theorem is referenced by: 9t8e72 9507 |
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