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Theorem nn0nepnfd 8640
Description: No standard nonnegative integer equals positive infinity, deduction form. (Contributed by AV, 10-Dec-2020.)
Hypothesis
Ref Expression
nn0xnn0d.1  |-  ( ph  ->  A  e.  NN0 )
Assertion
Ref Expression
nn0nepnfd  |-  ( ph  ->  A  =/= +oo )

Proof of Theorem nn0nepnfd
StepHypRef Expression
1 nn0xnn0d.1 . 2  |-  ( ph  ->  A  e.  NN0 )
2 nn0nepnf 8638 . 2  |-  ( A  e.  NN0  ->  A  =/= +oo )
31, 2syl 14 1  |-  ( ph  ->  A  =/= +oo )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434    =/= wne 2249   +oocpnf 7422   NN0cn0 8565
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-13 1445  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3922  ax-un 4224  ax-cnex 7339  ax-resscn 7340  ax-1re 7342  ax-addrcl 7345  ax-rnegex 7357
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ne 2250  df-nel 2345  df-ral 2358  df-rex 2359  df-rab 2362  df-v 2614  df-un 2988  df-in 2990  df-ss 2997  df-pw 3408  df-sn 3428  df-uni 3628  df-int 3663  df-pnf 7427  df-inn 8317  df-n0 8566
This theorem is referenced by: (None)
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