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Mirrors > Home > ILE Home > Th. List > 8re | GIF version |
Description: The number 8 is real. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
8re | ⊢ 8 ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-8 7979 | . 2 ⊢ 8 = (7 + 1) | |
2 | 7re 7998 | . . 3 ⊢ 7 ∈ ℝ | |
3 | 1re 7026 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7040 | . 2 ⊢ (7 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2110 | 1 ⊢ 8 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1393 (class class class)co 5512 ℝcr 6888 1c1 6890 + caddc 6892 7c7 7969 8c8 7970 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 ax-1re 6978 ax-addrcl 6981 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-clel 2036 df-2 7973 df-3 7974 df-4 7975 df-5 7976 df-6 7977 df-7 7978 df-8 7979 |
This theorem is referenced by: 8cn 8001 9re 8002 9pos 8020 6lt8 8108 5lt8 8109 4lt8 8110 3lt8 8111 2lt8 8112 1lt8 8113 8lt9 8114 7lt9 8115 8lt10 8123 7lt10 8124 8th4div3 8144 |
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