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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 12548 | . 2 ⊢ 9 ∈ ℕ0 | |
2 | 7nn0 12546 | . 2 ⊢ 7 ∈ ℕ0 | |
3 | 6nn0 12545 | . 2 ⊢ 6 ∈ ℕ0 | |
4 | df-8 12333 | . 2 ⊢ 8 = (7 + 1) | |
5 | df-7 12332 | . 2 ⊢ 7 = (6 + 1) | |
6 | 9p7e16 12823 | . 2 ⊢ (9 + 7) = ;16 | |
7 | 1, 2, 3, 4, 5, 6 | 6p5lem 12801 | 1 ⊢ (9 + 8) = ;17 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 (class class class)co 7431 1c1 11154 + caddc 11156 6c6 12323 7c7 12324 8c8 12325 9c9 12326 ;cdc 12731 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-11 2155 ax-12 2175 ax-ext 2706 ax-sep 5302 ax-nul 5312 ax-pow 5371 ax-pr 5438 ax-un 7754 ax-resscn 11210 ax-1cn 11211 ax-icn 11212 ax-addcl 11213 ax-addrcl 11214 ax-mulcl 11215 ax-mulrcl 11216 ax-mulcom 11217 ax-addass 11218 ax-mulass 11219 ax-distr 11220 ax-i2m1 11221 ax-1ne0 11222 ax-1rid 11223 ax-rnegex 11224 ax-rrecex 11225 ax-cnre 11226 ax-pre-lttri 11227 ax-pre-lttrn 11228 ax-pre-ltadd 11229 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3or 1087 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-nf 1781 df-sb 2063 df-mo 2538 df-eu 2567 df-clab 2713 df-cleq 2727 df-clel 2814 df-nfc 2890 df-ne 2939 df-nel 3045 df-ral 3060 df-rex 3069 df-reu 3379 df-rab 3434 df-v 3480 df-sbc 3792 df-csb 3909 df-dif 3966 df-un 3968 df-in 3970 df-ss 3980 df-pss 3983 df-nul 4340 df-if 4532 df-pw 4607 df-sn 4632 df-pr 4634 df-op 4638 df-uni 4913 df-iun 4998 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5583 df-eprel 5589 df-po 5597 df-so 5598 df-fr 5641 df-we 5643 df-xp 5695 df-rel 5696 df-cnv 5697 df-co 5698 df-dm 5699 df-rn 5700 df-res 5701 df-ima 5702 df-pred 6323 df-ord 6389 df-on 6390 df-lim 6391 df-suc 6392 df-iota 6516 df-fun 6565 df-fn 6566 df-f 6567 df-f1 6568 df-fo 6569 df-f1o 6570 df-fv 6571 df-ov 7434 df-om 7888 df-2nd 8014 df-frecs 8305 df-wrecs 8336 df-recs 8410 df-rdg 8449 df-er 8744 df-en 8985 df-dom 8986 df-sdom 8987 df-pnf 11295 df-mnf 11296 df-ltxr 11298 df-nn 12265 df-2 12327 df-3 12328 df-4 12329 df-5 12330 df-6 12331 df-7 12332 df-8 12333 df-9 12334 df-n0 12525 df-dec 12732 |
This theorem is referenced by: 9p9e18 12825 9t3e27 12854 37prm 17155 317prm 17160 2503lem2 17172 2503lem3 17173 fmtno4nprmfac193 47499 127prm 47524 |
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