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Mirrors > Home > ILE Home > Th. List > 7re | GIF version |
Description: The number 7 is real. (Contributed by NM, 27-May-1999.) |
Ref | Expression |
---|---|
7re | ⊢ 7 ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-7 8752 | . 2 ⊢ 7 = (6 + 1) | |
2 | 6re 8769 | . . 3 ⊢ 6 ∈ ℝ | |
3 | 1re 7733 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7747 | . 2 ⊢ (6 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2190 | 1 ⊢ 7 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1465 (class class class)co 5742 ℝcr 7587 1c1 7589 + caddc 7591 6c6 8743 7c7 8744 |
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 |
This theorem is referenced by: 7cn 8772 8re 8773 8pos 8791 5lt7 8873 4lt7 8874 3lt7 8875 2lt7 8876 1lt7 8877 7lt8 8878 6lt8 8879 7lt9 8886 6lt9 8887 7lt10 9282 6lt10 9283 |
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