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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 8964 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 5880 | . . . 4 ⊢ (5 + 2) = (5 + (1 + 1)) |
3 | 5cn 8985 | . . . . 5 ⊢ 5 ∈ ℂ | |
4 | ax-1cn 7892 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 7953 | . . . 4 ⊢ ((5 + 1) + 1) = (5 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2201 | . . 3 ⊢ (5 + 2) = ((5 + 1) + 1) |
7 | df-6 8968 | . . . 4 ⊢ 6 = (5 + 1) | |
8 | 7 | oveq1i 5879 | . . 3 ⊢ (6 + 1) = ((5 + 1) + 1) |
9 | 6, 8 | eqtr4i 2201 | . 2 ⊢ (5 + 2) = (6 + 1) |
10 | df-7 8969 | . 2 ⊢ 7 = (6 + 1) | |
11 | 9, 10 | eqtr4i 2201 | 1 ⊢ (5 + 2) = 7 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5869 1c1 7800 + caddc 7802 2c2 8956 5c5 8959 6c6 8960 7c7 8961 |
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 7891 ax-1cn 7892 ax-1re 7893 ax-addrcl 7896 ax-addass 7901 |
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 5174 df-fv 5220 df-ov 5872 df-2 8964 df-3 8965 df-4 8966 df-5 8967 df-6 8968 df-7 8969 |
This theorem is referenced by: 5p3e8 9052 |
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