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Mirrors > Home > ILE Home > Th. List > 7p2e9 | GIF version |
Description: 7 + 2 = 9. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
7p2e9 | ⊢ (7 + 2) = 9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8954 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 5879 | . . . 4 ⊢ (7 + 2) = (7 + (1 + 1)) |
3 | 7cn 8979 | . . . . 5 ⊢ 7 ∈ ℂ | |
4 | ax-1cn 7882 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 7943 | . . . 4 ⊢ ((7 + 1) + 1) = (7 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2201 | . . 3 ⊢ (7 + 2) = ((7 + 1) + 1) |
7 | df-8 8960 | . . . 4 ⊢ 8 = (7 + 1) | |
8 | 7 | oveq1i 5878 | . . 3 ⊢ (8 + 1) = ((7 + 1) + 1) |
9 | 6, 8 | eqtr4i 2201 | . 2 ⊢ (7 + 2) = (8 + 1) |
10 | df-9 8961 | . 2 ⊢ 9 = (8 + 1) | |
11 | 9, 10 | eqtr4i 2201 | 1 ⊢ (7 + 2) = 9 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5868 1c1 7790 + caddc 7792 2c2 8946 7c7 8951 8c8 8952 9c9 8953 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-resscn 7881 ax-1cn 7882 ax-1re 7883 ax-addrcl 7886 ax-addass 7891 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-iota 5173 df-fv 5219 df-ov 5871 df-2 8954 df-3 8955 df-4 8956 df-5 8957 df-6 8958 df-7 8959 df-8 8960 df-9 8961 |
This theorem is referenced by: 7p3e10 9434 7t7e49 9473 cos2bnd 11739 |
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