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Mirrors > Home > ILE Home > Th. List > 8p6e14 | GIF version |
Description: 8 + 6 = 14. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
8p6e14 | ⊢ (8 + 6) = ;14 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 8nn0 8430 | . 2 ⊢ 8 ∈ ℕ0 | |
2 | 5nn0 8427 | . 2 ⊢ 5 ∈ ℕ0 | |
3 | 3nn0 8425 | . 2 ⊢ 3 ∈ ℕ0 | |
4 | df-6 8221 | . 2 ⊢ 6 = (5 + 1) | |
5 | df-4 8219 | . 2 ⊢ 4 = (3 + 1) | |
6 | 8p5e13 8692 | . 2 ⊢ (8 + 5) = ;13 | |
7 | 1, 2, 3, 4, 5, 6 | 6p5lem 8679 | 1 ⊢ (8 + 6) = ;14 |
Colors of variables: wff set class |
Syntax hints: = wceq 1285 (class class class)co 5563 1c1 7096 + caddc 7098 3c3 8209 4c4 8210 5c5 8211 6c6 8212 8c8 8214 ;cdc 8610 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3916 ax-pow 3968 ax-pr 3992 ax-setind 4308 ax-cnex 7181 ax-resscn 7182 ax-1cn 7183 ax-1re 7184 ax-icn 7185 ax-addcl 7186 ax-addrcl 7187 ax-mulcl 7188 ax-addcom 7190 ax-mulcom 7191 ax-addass 7192 ax-mulass 7193 ax-distr 7194 ax-i2m1 7195 ax-1rid 7197 ax-0id 7198 ax-rnegex 7199 ax-cnre 7201 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-fal 1291 df-nf 1391 df-sb 1688 df-eu 1946 df-mo 1947 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ne 2250 df-ral 2358 df-rex 2359 df-reu 2360 df-rab 2362 df-v 2612 df-sbc 2825 df-dif 2984 df-un 2986 df-in 2988 df-ss 2995 df-pw 3402 df-sn 3422 df-pr 3423 df-op 3425 df-uni 3622 df-int 3657 df-br 3806 df-opab 3860 df-id 4076 df-xp 4397 df-rel 4398 df-cnv 4399 df-co 4400 df-dm 4401 df-iota 4917 df-fun 4954 df-fv 4960 df-riota 5519 df-ov 5566 df-oprab 5567 df-mpt2 5568 df-sub 7400 df-inn 8159 df-2 8217 df-3 8218 df-4 8219 df-5 8220 df-6 8221 df-7 8222 df-8 8223 df-9 8224 df-n0 8408 df-dec 8611 |
This theorem is referenced by: 8p7e15 8694 6t4e24 8715 8t3e24 8725 8t8e64 8730 |
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