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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 8103 | . 2 ⊢ 7 = (6 + 1) | |
2 | 6re 8120 | . . 3 ⊢ 6 ∈ ℝ | |
3 | 1re 7118 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7132 | . 2 ⊢ (6 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2151 | 1 ⊢ 7 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1433 (class class class)co 5532 ℝcr 6980 1c1 6982 + caddc 6984 6c6 8093 7c7 8094 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 ax-ext 2063 ax-1re 7070 ax-addrcl 7073 |
This theorem depends on definitions: df-bi 115 df-cleq 2074 df-clel 2077 df-2 8098 df-3 8099 df-4 8100 df-5 8101 df-6 8102 df-7 8103 |
This theorem is referenced by: 7cn 8123 8re 8124 8pos 8142 5lt7 8217 4lt7 8218 3lt7 8219 2lt7 8220 1lt7 8221 7lt8 8222 6lt8 8223 7lt9 8230 6lt9 8231 7lt10 8609 6lt10 8610 |
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