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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 7978 | . 2 ⊢ 7 = (6 + 1) | |
2 | 6re 7996 | . . 3 ⊢ 6 ∈ ℝ | |
3 | 1re 7026 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7040 | . 2 ⊢ (6 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2110 | 1 ⊢ 7 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1393 (class class class)co 5512 ℝcr 6888 1c1 6890 + caddc 6892 6c6 7968 7c7 7969 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 ax-1re 6978 ax-addrcl 6981 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-clel 2036 df-2 7973 df-3 7974 df-4 7975 df-5 7976 df-6 7977 df-7 7978 |
This theorem is referenced by: 7cn 7999 8re 8000 8pos 8019 5lt7 8102 4lt7 8103 3lt7 8104 2lt7 8105 1lt7 8106 7lt8 8107 6lt8 8108 7lt9 8115 6lt9 8116 7lt10 8124 6lt10 8125 |
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