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Theorem renepnfd 9128
Description: No (finite) real equals plus infinity. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rexrd.1  |-  ( ph  ->  A  e.  RR )
Assertion
Ref Expression
renepnfd  |-  ( ph  ->  A  =/=  +oo )

Proof of Theorem renepnfd
StepHypRef Expression
1 rexrd.1 . 2  |-  ( ph  ->  A  e.  RR )
2 renepnf 9125 . 2  |-  ( A  e.  RR  ->  A  =/=  +oo )
31, 2syl 16 1  |-  ( ph  ->  A  =/=  +oo )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725    =/= wne 2599   RRcr 8982    +oocpnf 9110
This theorem is referenced by:  xaddnepnf  10814  dvfsumrlimge0  19907  dvfsumrlim  19908  dvfsumrlim2  19909  logno1  20520
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4323  ax-nul 4331  ax-pow 4370  ax-pr 4396  ax-un 4694  ax-resscn 9040
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-nel 2602  df-rex 2704  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-pw 3794  df-sn 3813  df-pr 3814  df-uni 4009  df-pnf 9115
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