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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 8900 | . 2 ⊢ 9 = (8 + 1) | |
2 | 8re 8919 | . . 3 ⊢ 8 ∈ ℝ | |
3 | 1re 7878 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7892 | . 2 ⊢ (8 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2230 | 1 ⊢ 9 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2128 (class class class)co 5825 ℝcr 7732 1c1 7734 + caddc 7736 8c8 8891 9c9 8892 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-4 1490 ax-17 1506 ax-ial 1514 ax-ext 2139 ax-1re 7827 ax-addrcl 7830 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 df-clel 2153 df-2 8893 df-3 8894 df-4 8895 df-5 8896 df-6 8897 df-7 8898 df-8 8899 df-9 8900 |
This theorem is referenced by: 9cn 8922 7lt9 9032 6lt9 9033 5lt9 9034 4lt9 9035 3lt9 9036 2lt9 9037 1lt9 9038 9lt10 9426 8lt10 9427 0.999... 11422 cos2bnd 11661 sincos2sgn 11666 setsmsdsg 12922 2logb9irr 13330 2logb9irrap 13336 |
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