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Mirrors > Home > ILE Home > Th. List > 5p2e7 | GIF version |
Description: 5 + 2 = 7. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
5p2e7 | ⊢ (5 + 2) = 7 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 9043 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 5930 | . . . 4 ⊢ (5 + 2) = (5 + (1 + 1)) |
3 | 5cn 9064 | . . . . 5 ⊢ 5 ∈ ℂ | |
4 | ax-1cn 7967 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 8029 | . . . 4 ⊢ ((5 + 1) + 1) = (5 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2217 | . . 3 ⊢ (5 + 2) = ((5 + 1) + 1) |
7 | df-6 9047 | . . . 4 ⊢ 6 = (5 + 1) | |
8 | 7 | oveq1i 5929 | . . 3 ⊢ (6 + 1) = ((5 + 1) + 1) |
9 | 6, 8 | eqtr4i 2217 | . 2 ⊢ (5 + 2) = (6 + 1) |
10 | df-7 9048 | . 2 ⊢ 7 = (6 + 1) | |
11 | 9, 10 | eqtr4i 2217 | 1 ⊢ (5 + 2) = 7 |
Colors of variables: wff set class |
Syntax hints: = wceq 1364 (class class class)co 5919 1c1 7875 + caddc 7877 2c2 9035 5c5 9038 6c6 9039 7c7 9040 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 ax-resscn 7966 ax-1cn 7967 ax-1re 7968 ax-addrcl 7971 ax-addass 7976 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-rex 2478 df-v 2762 df-un 3158 df-in 3160 df-ss 3167 df-sn 3625 df-pr 3626 df-op 3628 df-uni 3837 df-br 4031 df-iota 5216 df-fv 5263 df-ov 5922 df-2 9043 df-3 9044 df-4 9045 df-5 9046 df-6 9047 df-7 9048 |
This theorem is referenced by: 5p3e8 9132 |
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