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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 8549 | . 2 ⊢ 7 = (6 + 1) | |
2 | 6re 8566 | . . 3 ⊢ 6 ∈ ℝ | |
3 | 1re 7550 | . . 3 ⊢ 1 ∈ ℝ | |
4 | 2, 3 | readdcli 7564 | . 2 ⊢ (6 + 1) ∈ ℝ |
5 | 1, 4 | eqeltri 2161 | 1 ⊢ 7 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1439 (class class class)co 5668 ℝcr 7412 1c1 7414 + caddc 7416 6c6 8540 7c7 8541 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-4 1446 ax-17 1465 ax-ial 1473 ax-ext 2071 ax-1re 7502 ax-addrcl 7505 |
This theorem depends on definitions: df-bi 116 df-cleq 2082 df-clel 2085 df-2 8544 df-3 8545 df-4 8546 df-5 8547 df-6 8548 df-7 8549 |
This theorem is referenced by: 7cn 8569 8re 8570 8pos 8588 5lt7 8664 4lt7 8665 3lt7 8666 2lt7 8667 1lt7 8668 7lt8 8669 6lt8 8670 7lt9 8677 6lt9 8678 7lt10 9072 6lt10 9073 |
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