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Theorem renepnfd 8026
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 8023 . 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 2160    =/= wne 2360   RRcr 7828   +oocpnf 8007
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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-13 2162  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-un 4448  ax-cnex 7920  ax-resscn 7921
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ne 2361  df-nel 2456  df-rex 2474  df-rab 2477  df-v 2754  df-in 3150  df-ss 3157  df-pw 3592  df-uni 3825  df-pnf 8012
This theorem is referenced by:  xaddnepnf  9876
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