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Mirrors > Home > ILE Home > Th. List > zrei | GIF version |
Description: An integer is a real number. (Contributed by NM, 14-Jul-2005.) |
Ref | Expression |
---|---|
zre.1 | ⊢ 𝐴 ∈ ℤ |
Ref | Expression |
---|---|
zrei | ⊢ 𝐴 ∈ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zre.1 | . 2 ⊢ 𝐴 ∈ ℤ | |
2 | zre 9051 | . 2 ⊢ (𝐴 ∈ ℤ → 𝐴 ∈ ℝ) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝐴 ∈ ℝ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1480 ℝcr 7612 ℤcz 9047 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-rab 2423 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 df-ov 5770 df-neg 7929 df-z 9048 |
This theorem is referenced by: dfuzi 9154 eluzaddi 9345 eluzsubi 9346 |
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