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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 8753 | . 2 ⊢ 8 = (7 + 1) | |
2 | 7re 8771 | . . 3 ⊢ 7 ∈ ℝ | |
3 | 1re 7733 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7747 | . 2 ⊢ (7 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2190 | 1 ⊢ 8 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 (class class class)co 5742 ℝcr 7587 1c1 7589 + caddc 7591 7c7 8744 8c8 8745 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 ax-1re 7682 ax-addrcl 7685 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-clel 2113 df-2 8747 df-3 8748 df-4 8749 df-5 8750 df-6 8751 df-7 8752 df-8 8753 |
This theorem is referenced by: 8cn 8774 9re 8775 9pos 8792 6lt8 8879 5lt8 8880 4lt8 8881 3lt8 8882 2lt8 8883 1lt8 8884 8lt9 8885 7lt9 8886 8th4div3 8907 8lt10 9281 7lt10 9282 ef01bndlem 11390 cos2bnd 11394 |
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