ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  renemnfd Unicode version

Theorem renemnfd 7600
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 7597 . 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 1439    =/= wne 2256   RRcr 7410   -oocmnf 7581
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-setind 4366  ax-cnex 7497  ax-resscn 7498
This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ne 2257  df-nel 2352  df-ral 2365  df-v 2622  df-dif 3002  df-un 3004  df-in 3006  df-ss 3013  df-pw 3435  df-sn 3456  df-pr 3457  df-uni 3660  df-pnf 7585  df-mnf 7586
This theorem is referenced by:  xnn0nemnf  8808
  Copyright terms: Public domain W3C validator