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Mirrors > Home > ILE Home > Th. List > 9p7e16 | Unicode version |
Description: 9 + 7 = 16. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
9p7e16 | ; |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9nn0 9138 | . 2 | |
2 | 6nn0 9135 | . 2 | |
3 | 5nn0 9134 | . 2 | |
4 | df-7 8921 | . 2 | |
5 | df-6 8920 | . 2 | |
6 | 9p6e15 9412 | . 2 ; | |
7 | 1, 2, 3, 4, 5, 6 | 6p5lem 9391 | 1 ; |
Colors of variables: wff set class |
Syntax hints: wceq 1343 (class class class)co 5842 c1 7754 caddc 7756 c5 8911 c6 8912 c7 8913 c9 8915 ;cdc 9322 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-14 2139 ax-ext 2147 ax-sep 4100 ax-pow 4153 ax-pr 4187 ax-setind 4514 ax-cnex 7844 ax-resscn 7845 ax-1cn 7846 ax-1re 7847 ax-icn 7848 ax-addcl 7849 ax-addrcl 7850 ax-mulcl 7851 ax-addcom 7853 ax-mulcom 7854 ax-addass 7855 ax-mulass 7856 ax-distr 7857 ax-i2m1 7858 ax-1rid 7860 ax-0id 7861 ax-rnegex 7862 ax-cnre 7864 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-fal 1349 df-nf 1449 df-sb 1751 df-eu 2017 df-mo 2018 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ne 2337 df-ral 2449 df-rex 2450 df-reu 2451 df-rab 2453 df-v 2728 df-sbc 2952 df-dif 3118 df-un 3120 df-in 3122 df-ss 3129 df-pw 3561 df-sn 3582 df-pr 3583 df-op 3585 df-uni 3790 df-int 3825 df-br 3983 df-opab 4044 df-id 4271 df-xp 4610 df-rel 4611 df-cnv 4612 df-co 4613 df-dm 4614 df-iota 5153 df-fun 5190 df-fv 5196 df-riota 5798 df-ov 5845 df-oprab 5846 df-mpo 5847 df-sub 8071 df-inn 8858 df-2 8916 df-3 8917 df-4 8918 df-5 8919 df-6 8920 df-7 8921 df-8 8922 df-9 8923 df-n0 9115 df-dec 9323 |
This theorem is referenced by: 9p8e17 9414 9t4e36 9445 |
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