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Mirrors > Home > ILE Home > Th. List > 5p5e10 | GIF version |
Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
5p5e10 | ⊢ (5 + 5) = ;10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-5 8238 | . . . 4 ⊢ 5 = (4 + 1) | |
2 | 1 | oveq2i 5575 | . . 3 ⊢ (5 + 5) = (5 + (4 + 1)) |
3 | 5cn 8256 | . . . 4 ⊢ 5 ∈ ℂ | |
4 | 4cn 8254 | . . . 4 ⊢ 4 ∈ ℂ | |
5 | ax-1cn 7201 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 7259 | . . 3 ⊢ ((5 + 4) + 1) = (5 + (4 + 1)) |
7 | 2, 6 | eqtr4i 2106 | . 2 ⊢ (5 + 5) = ((5 + 4) + 1) |
8 | 5p4e9 8317 | . . 3 ⊢ (5 + 4) = 9 | |
9 | 8 | oveq1i 5574 | . 2 ⊢ ((5 + 4) + 1) = (9 + 1) |
10 | 9p1e10 8630 | . 2 ⊢ (9 + 1) = ;10 | |
11 | 7, 9, 10 | 3eqtri 2107 | 1 ⊢ (5 + 5) = ;10 |
Colors of variables: wff set class |
Syntax hints: = wceq 1285 (class class class)co 5564 0cc0 7113 1c1 7114 + caddc 7116 4c4 8228 5c5 8229 9c9 8233 ;cdc 8628 |
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-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-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3916 ax-cnex 7199 ax-resscn 7200 ax-1cn 7201 ax-1re 7202 ax-icn 7203 ax-addcl 7204 ax-addrcl 7205 ax-mulcl 7206 ax-mulcom 7209 ax-addass 7210 ax-mulass 7211 ax-distr 7212 ax-1rid 7215 ax-0id 7216 ax-cnre 7219 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ral 2358 df-rex 2359 df-rab 2362 df-v 2612 df-un 2986 df-in 2988 df-ss 2995 df-sn 3422 df-pr 3423 df-op 3425 df-uni 3622 df-int 3657 df-br 3806 df-iota 4917 df-fv 4960 df-ov 5567 df-inn 8177 df-2 8235 df-3 8236 df-4 8237 df-5 8238 df-6 8239 df-7 8240 df-8 8241 df-9 8242 df-dec 8629 |
This theorem is referenced by: 5t2e10 8727 5t4e20 8729 |
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