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Theorem renepnfd 7599
Description: No (finite) real equals plus infinity. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rexrd.1 (𝜑𝐴 ∈ ℝ)
Assertion
Ref Expression
renepnfd (𝜑𝐴 ≠ +∞)

Proof of Theorem renepnfd
StepHypRef Expression
1 rexrd.1 . 2 (𝜑𝐴 ∈ ℝ)
2 renepnf 7596 . 2 (𝐴 ∈ ℝ → 𝐴 ≠ +∞)
31, 2syl 14 1 (𝜑𝐴 ≠ +∞)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1439  wne 2256  cr 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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