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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 8929 | . 2 ⊢ 7 = (6 + 1) | |
2 | 6re 8946 | . . 3 ⊢ 6 ∈ ℝ | |
3 | 1re 7906 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7920 | . 2 ⊢ (6 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2243 | 1 ⊢ 7 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2141 (class class class)co 5850 ℝcr 7760 1c1 7762 + caddc 7764 6c6 8920 7c7 8921 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 ax-ext 2152 ax-1re 7855 ax-addrcl 7858 |
This theorem depends on definitions: df-bi 116 df-cleq 2163 df-clel 2166 df-2 8924 df-3 8925 df-4 8926 df-5 8927 df-6 8928 df-7 8929 |
This theorem is referenced by: 7cn 8949 8re 8950 8pos 8968 5lt7 9050 4lt7 9051 3lt7 9052 2lt7 9053 1lt7 9054 7lt8 9055 6lt8 9056 7lt9 9063 6lt9 9064 7lt10 9462 6lt10 9463 lgsdir2lem1 13682 |
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