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Theorem nn0nepnfd 9018
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 9016 . 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 1465    =/= wne 2285   +oocpnf 7765   NN0cn0 8945
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 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-13 1476  ax-14 1477  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-un 4325  ax-cnex 7679  ax-resscn 7680  ax-1re 7682  ax-addrcl 7685  ax-rnegex 7697
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ne 2286  df-nel 2381  df-ral 2398  df-rex 2399  df-rab 2402  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-pw 3482  df-sn 3503  df-uni 3707  df-int 3742  df-pnf 7770  df-inn 8689  df-n0 8946
This theorem is referenced by: (None)
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