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Theorem renemnfd 7840
Description: No real equals minus infinity. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rexrd.1  |-  ( ph  ->  A  e.  RR )
Assertion
Ref Expression
renemnfd  |-  ( ph  ->  A  =/= -oo )

Proof of Theorem renemnfd
StepHypRef Expression
1 rexrd.1 . 2  |-  ( ph  ->  A  e.  RR )
2 renemnf 7837 . 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 1481    =/= wne 2309   RRcr 7642   -oocmnf 7821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-setind 4459  ax-cnex 7734  ax-resscn 7735
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ne 2310  df-nel 2405  df-ral 2422  df-v 2691  df-dif 3077  df-un 3079  df-in 3081  df-ss 3088  df-pw 3516  df-sn 3537  df-pr 3538  df-uni 3744  df-pnf 7825  df-mnf 7826
This theorem is referenced by:  xnn0nemnf  9074  xaddnemnf  9669  xposdif  9694  xleaddadd  9699  xrbdtri  11076
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