| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > zrei | Structured version Visualization version GIF version | ||
| Description: An integer is a real number. (Contributed by NM, 14-Jul-2005.) |
| Ref | Expression |
|---|---|
| zrei.1 | ⊢ 𝐴 ∈ ℤ |
| Ref | Expression |
|---|---|
| zrei | ⊢ 𝐴 ∈ ℝ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | zrei.1 | . 2 ⊢ 𝐴 ∈ ℤ | |
| 2 | zre 12617 | . 2 ⊢ (𝐴 ∈ ℤ → 𝐴 ∈ ℝ) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ ℝ |
| Colors of variables: wff setvar class |
| Syntax hints: ∈ wcel 2108 ℝcr 11154 ℤcz 12613 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3or 1088 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-iota 6514 df-fv 6569 df-ov 7434 df-neg 11495 df-z 12614 |
| This theorem is referenced by: dfuzi 12709 eluzaddiOLD 12910 eluzsubiOLD 12912 dvdslelem 16346 divalglem1 16431 divalglem6 16435 divalglem9 16438 gcdaddmlem 16561 basellem9 27132 axlowdimlem16 28972 poimirlem17 37644 poimirlem19 37646 poimirlem20 37647 fdc 37752 jm2.27dlem2 43022 |
| Copyright terms: Public domain | W3C validator |