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Theorem renepnfd 9061
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 9058 . 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 1717    =/= wne 2543   RRcr 8915    +oocpnf 9043
This theorem is referenced by:  xaddnepnf  10746  dvfsumrlimge0  19774  dvfsumrlim  19775  dvfsumrlim2  19776  logno1  20387
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-13 1719  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361  ax-sep 4264  ax-nul 4272  ax-pow 4311  ax-pr 4337  ax-un 4634  ax-resscn 8973
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-nel 2546  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-pw 3737  df-sn 3756  df-pr 3757  df-uni 3951  df-pnf 9048
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