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Mirrors > Home > ILE Home > Th. List > 6p6e12 | GIF version |
Description: 6 + 6 = 12. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
6p6e12 | ⊢ (6 + 6) = ;12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6nn0 9156 | . 2 ⊢ 6 ∈ ℕ0 | |
2 | 5nn0 9155 | . 2 ⊢ 5 ∈ ℕ0 | |
3 | 1nn0 9151 | . 2 ⊢ 1 ∈ ℕ0 | |
4 | df-6 8941 | . 2 ⊢ 6 = (5 + 1) | |
5 | df-2 8937 | . 2 ⊢ 2 = (1 + 1) | |
6 | 6p5e11 9415 | . 2 ⊢ (6 + 5) = ;11 | |
7 | 1, 2, 3, 4, 5, 6 | 6p5lem 9412 | 1 ⊢ (6 + 6) = ;12 |
Colors of variables: wff set class |
Syntax hints: = wceq 1348 (class class class)co 5853 1c1 7775 + caddc 7777 2c2 8929 5c5 8932 6c6 8933 ;cdc 9343 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-setind 4521 ax-cnex 7865 ax-resscn 7866 ax-1cn 7867 ax-1re 7868 ax-icn 7869 ax-addcl 7870 ax-addrcl 7871 ax-mulcl 7872 ax-addcom 7874 ax-mulcom 7875 ax-addass 7876 ax-mulass 7877 ax-distr 7878 ax-i2m1 7879 ax-1rid 7881 ax-0id 7882 ax-rnegex 7883 ax-cnre 7885 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-ral 2453 df-rex 2454 df-reu 2455 df-rab 2457 df-v 2732 df-sbc 2956 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-int 3832 df-br 3990 df-opab 4051 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-iota 5160 df-fun 5200 df-fv 5206 df-riota 5809 df-ov 5856 df-oprab 5857 df-mpo 5858 df-sub 8092 df-inn 8879 df-2 8937 df-3 8938 df-4 8939 df-5 8940 df-6 8941 df-7 8942 df-8 8943 df-9 8944 df-n0 9136 df-dec 9344 |
This theorem is referenced by: 6t2e12 9446 |
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