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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 12615 | . 2 ⊢ (𝐴 ∈ ℤ → 𝐴 ∈ ℝ) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ ℝ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2106 ℝcr 11152 ℤcz 12611 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3or 1087 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-rab 3434 df-v 3480 df-dif 3966 df-un 3968 df-ss 3980 df-nul 4340 df-if 4532 df-sn 4632 df-pr 4634 df-op 4638 df-uni 4913 df-br 5149 df-iota 6516 df-fv 6571 df-ov 7434 df-neg 11493 df-z 12612 |
This theorem is referenced by: dfuzi 12707 eluzaddiOLD 12908 eluzsubiOLD 12910 dvdslelem 16343 divalglem1 16428 divalglem6 16432 divalglem9 16435 gcdaddmlem 16558 basellem9 27147 axlowdimlem16 28987 poimirlem17 37624 poimirlem19 37626 poimirlem20 37627 fdc 37732 jm2.27dlem2 42999 |
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