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| Description: The number 7 is real. (Contributed by NM, 27-May-1999.) | 
| Ref | Expression | 
|---|---|
| 7re | ⊢ 7 ∈ ℝ | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-7 12335 | . 2 ⊢ 7 = (6 + 1) | |
| 2 | 6re 12357 | . . 3 ⊢ 6 ∈ ℝ | |
| 3 | 1re 11262 | . . 3 ⊢ 1 ∈ ℝ | |
| 4 | 2, 3 | readdcli 11277 | . 2 ⊢ (6 + 1) ∈ ℝ | 
| 5 | 1, 4 | eqeltri 2836 | 1 ⊢ 7 ∈ ℝ | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∈ wcel 2107 (class class class)co 7432 ℝcr 11155 1c1 11157 + caddc 11159 6c6 12326 7c7 12327 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 ax-1cn 11214 ax-icn 11215 ax-addcl 11216 ax-addrcl 11217 ax-mulcl 11218 ax-mulrcl 11219 ax-i2m1 11224 ax-1ne0 11225 ax-rrecex 11228 ax-cnre 11229 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1542 df-fal 1552 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-ne 2940 df-ral 3061 df-rex 3070 df-rab 3436 df-v 3481 df-dif 3953 df-un 3955 df-ss 3967 df-nul 4333 df-if 4525 df-sn 4626 df-pr 4628 df-op 4632 df-uni 4907 df-br 5143 df-iota 6513 df-fv 6568 df-ov 7435 df-2 12330 df-3 12331 df-4 12332 df-5 12333 df-6 12334 df-7 12335 | 
| This theorem is referenced by: 8re 12363 8pos 12379 5lt7 12454 4lt7 12455 3lt7 12456 2lt7 12457 1lt7 12458 7lt8 12459 6lt8 12460 7lt9 12467 6lt9 12468 7lt10 12868 6lt10 12869 bposlem8 27336 lgsdir2lem1 27370 hgt750lem2 34668 hgt750leme 34674 problem4 35674 60gcd7e1 42007 lcmineqlem 42054 3lexlogpow5ineq1 42056 3lexlogpow5ineq2 42057 3lexlogpow5ineq4 42058 3lexlogpow5ineq3 42059 aks4d1p1p3 42071 aks4d1p1p2 42072 aks4d1p1p4 42073 aks4d1p1p7 42076 aks4d1p2 42079 aks4d1p3 42080 7rp 42341 mod42tp1mod8 47594 stgoldbwt 47768 sbgoldbwt 47769 nnsum3primesle9 47786 nnsum4primesoddALTV 47789 evengpoap3 47791 bgoldbtbndlem1 47797 bgoldbtbnd 47801 | 
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