![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 8159 | . 2 ⊢ 7 = (6 + 1) | |
2 | 6re 8176 | . . 3 ⊢ 6 ∈ ℝ | |
3 | 1re 7169 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7183 | . 2 ⊢ (6 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2152 | 1 ⊢ 7 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1434 (class class class)co 5537 ℝcr 7031 1c1 7033 + caddc 7035 6c6 8149 7c7 8150 |
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 1377 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-4 1441 ax-17 1460 ax-ial 1468 ax-ext 2064 ax-1re 7121 ax-addrcl 7124 |
This theorem depends on definitions: df-bi 115 df-cleq 2075 df-clel 2078 df-2 8154 df-3 8155 df-4 8156 df-5 8157 df-6 8158 df-7 8159 |
This theorem is referenced by: 7cn 8179 8re 8180 8pos 8198 5lt7 8273 4lt7 8274 3lt7 8275 2lt7 8276 1lt7 8277 7lt8 8278 6lt8 8279 7lt9 8286 6lt9 8287 7lt10 8679 6lt10 8680 |
Copyright terms: Public domain | W3C validator |