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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 11258 | . 2 ⊢ (𝐴 ∈ ℤ → 𝐴 ∈ ℝ) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ ℝ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 ℝcr 9814 ℤcz 11254 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3or 1032 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rex 2902 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-iota 5768 df-fv 5812 df-ov 6552 df-neg 10148 df-z 11255 |
This theorem is referenced by: dfuzi 11344 eluzaddi 11590 eluzsubi 11591 dvdslelem 14869 divalglem1 14955 divalglem6 14959 divalglem9 14962 gcdaddmlem 15083 basellem9 24615 axlowdimlem16 25637 poimirlem17 32596 poimirlem19 32598 poimirlem20 32599 fdc 32711 jm2.27dlem2 36595 |
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