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Theorem renepnfd 9549
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 9546 . 2  |-  ( A  e.  RR  ->  A  =/= +oo )
31, 2syl 16 1  |-  ( ph  ->  A  =/= +oo )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1758    =/= wne 2648   RRcr 9396   +oocpnf 9530
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4524  ax-nul 4532  ax-pow 4581  ax-pr 4642  ax-un 6485  ax-resscn 9454
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-nel 2651  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-pw 3973  df-sn 3989  df-pr 3991  df-uni 4203  df-pnf 9535
This theorem is referenced by:  xaddnepnf  11320  dvfsumrlimge0  21645  dvfsumrlim  21646  dvfsumrlim2  21647  logno1  22224
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