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Theorem renepnfd 9698
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 9695 . 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 1872    =/= wne 2614   RRcr 9545   +oocpnf 9679
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-8 1874  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546  ax-nul 4555  ax-pow 4602  ax-pr 4660  ax-un 6597  ax-resscn 9603
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-nel 2617  df-rex 2777  df-rab 2780  df-v 3082  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-pw 3983  df-sn 3999  df-pr 4001  df-uni 4220  df-pnf 9684
This theorem is referenced by:  xaddnepnf  11535  dvfsumrlimge0  22980  dvfsumrlim  22981  dvfsumrlim2  22982  logno1  23579
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