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Mirrors > Home > ILE Home > Th. List > 9re | GIF version |
Description: The number 9 is real. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
9re | ⊢ 9 ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-9 7980 | . 2 ⊢ 9 = (8 + 1) | |
2 | 8re 8000 | . . 3 ⊢ 8 ∈ ℝ | |
3 | 1re 7026 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7040 | . 2 ⊢ (8 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2110 | 1 ⊢ 9 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1393 (class class class)co 5512 ℝcr 6888 1c1 6890 + caddc 6892 8c8 7970 9c9 7971 |
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 df-9 7980 |
This theorem is referenced by: 9cn 8003 10re 8004 10pos 8021 7lt9 8115 6lt9 8116 5lt9 8117 4lt9 8118 3lt9 8119 2lt9 8120 1lt9 8121 9lt10 8122 8lt10 8123 |
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