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Theorem renepnfd 8021
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 8018 . 2  |-  ( A  e.  RR  ->  A  =/= +oo )
31, 2syl 14 1  |-  ( ph  ->  A  =/= +oo )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2158    =/= wne 2357   RRcr 7823   +oocpnf 8002
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-13 2160  ax-14 2161  ax-ext 2169  ax-sep 4133  ax-un 4445  ax-cnex 7915  ax-resscn 7916
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-ne 2358  df-nel 2453  df-rex 2471  df-rab 2474  df-v 2751  df-in 3147  df-ss 3154  df-pw 3589  df-uni 3822  df-pnf 8007
This theorem is referenced by:  xaddnepnf  9871
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