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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 9001 | . 2 ⊢ 7 = (6 + 1) | |
2 | 6re 9018 | . . 3 ⊢ 6 ∈ ℝ | |
3 | 1re 7974 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7988 | . 2 ⊢ (6 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2262 | 1 ⊢ 7 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 (class class class)co 5891 ℝcr 7828 1c1 7830 + caddc 7832 6c6 8992 7c7 8993 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 ax-ext 2171 ax-1re 7923 ax-addrcl 7926 |
This theorem depends on definitions: df-bi 117 df-cleq 2182 df-clel 2185 df-2 8996 df-3 8997 df-4 8998 df-5 8999 df-6 9000 df-7 9001 |
This theorem is referenced by: 7cn 9021 8re 9022 8pos 9040 5lt7 9122 4lt7 9123 3lt7 9124 2lt7 9125 1lt7 9126 7lt8 9127 6lt8 9128 7lt9 9135 6lt9 9136 7lt10 9534 6lt10 9535 lgsdir2lem1 14813 |
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