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Theorem renepnfd 9592
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 9589 . 2  |-  ( A  e.  RR  ->  A  =/= +oo )
31, 2syl 17 1  |-  ( ph  ->  A  =/= +oo )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1840    =/= wne 2596   RRcr 9439   +oocpnf 9573
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-8 1842  ax-9 1844  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378  ax-sep 4514  ax-nul 4522  ax-pow 4569  ax-pr 4627  ax-un 6528  ax-resscn 9497
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 974  df-tru 1406  df-ex 1632  df-nf 1636  df-sb 1762  df-clab 2386  df-cleq 2392  df-clel 2395  df-nfc 2550  df-ne 2598  df-nel 2599  df-rex 2757  df-rab 2760  df-v 3058  df-dif 3414  df-un 3416  df-in 3418  df-ss 3425  df-nul 3736  df-pw 3954  df-sn 3970  df-pr 3972  df-uni 4189  df-pnf 9578
This theorem is referenced by:  xaddnepnf  11403  dvfsumrlimge0  22613  dvfsumrlim  22614  dvfsumrlim2  22615  logno1  23201
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