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 11986 | . 2 ⊢ (𝐴 ∈ ℤ → 𝐴 ∈ ℝ) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ ℝ |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2114 ℝcr 10536 ℤcz 11982 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3or 1084 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rab 3147 df-v 3496 df-dif 3939 df-un 3941 df-in 3943 df-ss 3952 df-nul 4292 df-if 4468 df-sn 4568 df-pr 4570 df-op 4574 df-uni 4839 df-br 5067 df-iota 6314 df-fv 6363 df-ov 7159 df-neg 10873 df-z 11983 |
This theorem is referenced by: dfuzi 12074 eluzaddi 12272 eluzsubi 12273 dvdslelem 15659 divalglem1 15745 divalglem6 15749 divalglem9 15752 gcdaddmlem 15872 basellem9 25666 axlowdimlem16 26743 poimirlem17 34924 poimirlem19 34926 poimirlem20 34927 fdc 35035 jm2.27dlem2 39627 |
Copyright terms: Public domain | W3C validator |