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Mirrors > Home > ILE Home > Th. List > 9p9e18 | GIF version |
Description: 9 + 9 = 18. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
9p9e18 | ⊢ (9 + 9) = ;18 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 9nn0 8899 | . 2 ⊢ 9 ∈ ℕ0 | |
2 | 8nn0 8898 | . 2 ⊢ 8 ∈ ℕ0 | |
3 | 7nn0 8897 | . 2 ⊢ 7 ∈ ℕ0 | |
4 | df-9 8690 | . 2 ⊢ 9 = (8 + 1) | |
5 | df-8 8689 | . 2 ⊢ 8 = (7 + 1) | |
6 | 9p8e17 9172 | . 2 ⊢ (9 + 8) = ;17 | |
7 | 1, 2, 3, 4, 5, 6 | 6p5lem 9149 | 1 ⊢ (9 + 9) = ;18 |
Colors of variables: wff set class |
Syntax hints: = wceq 1312 (class class class)co 5726 1c1 7542 + caddc 7544 7c7 8680 8c8 8681 9c9 8682 ;cdc 9080 |
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 586 ax-in2 587 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 ax-setind 4410 ax-cnex 7630 ax-resscn 7631 ax-1cn 7632 ax-1re 7633 ax-icn 7634 ax-addcl 7635 ax-addrcl 7636 ax-mulcl 7637 ax-addcom 7639 ax-mulcom 7640 ax-addass 7641 ax-mulass 7642 ax-distr 7643 ax-i2m1 7644 ax-1rid 7646 ax-0id 7647 ax-rnegex 7648 ax-cnre 7650 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-fal 1318 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ne 2281 df-ral 2393 df-rex 2394 df-reu 2395 df-rab 2397 df-v 2657 df-sbc 2877 df-dif 3037 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-uni 3701 df-int 3736 df-br 3894 df-opab 3948 df-id 4173 df-xp 4503 df-rel 4504 df-cnv 4505 df-co 4506 df-dm 4507 df-iota 5044 df-fun 5081 df-fv 5087 df-riota 5682 df-ov 5729 df-oprab 5730 df-mpo 5731 df-sub 7852 df-inn 8625 df-2 8683 df-3 8684 df-4 8685 df-5 8686 df-6 8687 df-7 8688 df-8 8689 df-9 8690 df-n0 8876 df-dec 9081 |
This theorem is referenced by: 9t2e18 9201 |
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