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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 7596 | . 2 ⊢ (𝐴 ∈ ℝ → 𝐴 ≠ +∞) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → 𝐴 ≠ +∞) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1439 ≠ wne 2256 ℝcr 7410 +∞cpnf 7580 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-13 1450 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-un 4269 ax-cnex 7497 ax-resscn 7498 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-fal 1296 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ne 2257 df-nel 2352 df-rex 2366 df-rab 2369 df-v 2622 df-in 3006 df-ss 3013 df-pw 3435 df-uni 3660 df-pnf 7585 |
This theorem is referenced by: (None) |
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