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Mirrors > Home > ILE Home > Th. List > renepnfd | GIF version |
Description: No (finite) real equals plus infinity. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rexrd.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
Ref | Expression |
---|---|
renepnfd | ⊢ (𝜑 → 𝐴 ≠ +∞) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexrd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
2 | renepnf 7166 | . 2 ⊢ (𝐴 ∈ ℝ → 𝐴 ≠ +∞) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → 𝐴 ≠ +∞) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1433 ≠ wne 2245 ℝcr 6980 +∞cpnf 7150 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-un 4188 ax-cnex 7067 ax-resscn 7068 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-nel 2340 df-rex 2354 df-rab 2357 df-v 2603 df-in 2979 df-ss 2986 df-pw 3384 df-uni 3602 df-pnf 7155 |
This theorem is referenced by: (None) |
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