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Mirrors > Home > MPE Home > Th. List > 9p8e17 | Structured version Visualization version GIF version |
Description: 9 + 8 = 17. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
9p8e17 | ⊢ (9 + 8) = ;17 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9nn0 11506 | . 2 ⊢ 9 ∈ ℕ0 | |
2 | 7nn0 11504 | . 2 ⊢ 7 ∈ ℕ0 | |
3 | 6nn0 11503 | . 2 ⊢ 6 ∈ ℕ0 | |
4 | df-8 11275 | . 2 ⊢ 8 = (7 + 1) | |
5 | df-7 11274 | . 2 ⊢ 7 = (6 + 1) | |
6 | 9p7e16 11815 | . 2 ⊢ (9 + 7) = ;16 | |
7 | 1, 2, 3, 4, 5, 6 | 6p5lem 11785 | 1 ⊢ (9 + 8) = ;17 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1630 (class class class)co 6811 1c1 10127 + caddc 10129 6c6 11264 7c7 11265 8c8 11266 9c9 11267 ;cdc 11683 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1869 ax-4 1884 ax-5 1986 ax-6 2052 ax-7 2088 ax-8 2139 ax-9 2146 ax-10 2166 ax-11 2181 ax-12 2194 ax-13 2389 ax-ext 2738 ax-sep 4931 ax-nul 4939 ax-pow 4990 ax-pr 5053 ax-un 7112 ax-resscn 10183 ax-1cn 10184 ax-icn 10185 ax-addcl 10186 ax-addrcl 10187 ax-mulcl 10188 ax-mulrcl 10189 ax-mulcom 10190 ax-addass 10191 ax-mulass 10192 ax-distr 10193 ax-i2m1 10194 ax-1ne0 10195 ax-1rid 10196 ax-rnegex 10197 ax-rrecex 10198 ax-cnre 10199 ax-pre-lttri 10200 ax-pre-lttrn 10201 ax-pre-ltadd 10202 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3or 1073 df-3an 1074 df-tru 1633 df-ex 1852 df-nf 1857 df-sb 2045 df-eu 2609 df-mo 2610 df-clab 2745 df-cleq 2751 df-clel 2754 df-nfc 2889 df-ne 2931 df-nel 3034 df-ral 3053 df-rex 3054 df-reu 3055 df-rab 3057 df-v 3340 df-sbc 3575 df-csb 3673 df-dif 3716 df-un 3718 df-in 3720 df-ss 3727 df-pss 3729 df-nul 4057 df-if 4229 df-pw 4302 df-sn 4320 df-pr 4322 df-tp 4324 df-op 4326 df-uni 4587 df-iun 4672 df-br 4803 df-opab 4863 df-mpt 4880 df-tr 4903 df-id 5172 df-eprel 5177 df-po 5185 df-so 5186 df-fr 5223 df-we 5225 df-xp 5270 df-rel 5271 df-cnv 5272 df-co 5273 df-dm 5274 df-rn 5275 df-res 5276 df-ima 5277 df-pred 5839 df-ord 5885 df-on 5886 df-lim 5887 df-suc 5888 df-iota 6010 df-fun 6049 df-fn 6050 df-f 6051 df-f1 6052 df-fo 6053 df-f1o 6054 df-fv 6055 df-ov 6814 df-om 7229 df-wrecs 7574 df-recs 7635 df-rdg 7673 df-er 7909 df-en 8120 df-dom 8121 df-sdom 8122 df-pnf 10266 df-mnf 10267 df-ltxr 10269 df-nn 11211 df-2 11269 df-3 11270 df-4 11271 df-5 11272 df-6 11273 df-7 11274 df-8 11275 df-9 11276 df-n0 11483 df-dec 11684 |
This theorem is referenced by: 9p9e18 11817 9t3e27 11854 37prm 16028 317prm 16033 2503lem2 16045 2503lem3 16046 fmtno4nprmfac193 41994 127prm 42023 |
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