Theorem nn0nepnfd 9262

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

Step	Hyp	Ref	Expression
1		nn0xnn0d.1	. 2 |- ( ph -> A e. NN0 )
2		nn0nepnf 9260	. 2 |- ( A e. NN0 -> A =/= +oo )
3	1, 2	syl 14	1 |- ( ph -> A =/= +oo )

Syntax hints:   -> wi 4   e. wcel 2158   =/= wne 2357   +oocpnf 8002   NN0cn0 9189

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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-13 2160  ax-14 2161  ax-ext 2169  ax-sep 4133  ax-un 4445  ax-cnex 7915  ax-resscn 7916  ax-1re 7918  ax-addrcl 7921  ax-rnegex 7933

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-ne 2358  df-nel 2453  df-ral 2470  df-rex 2471  df-rab 2474  df-v 2751  df-un 3145  df-in 3147  df-ss 3154  df-pw 3589  df-sn 3610  df-uni 3822  df-int 3857  df-pnf 8007  df-inn 8933  df-n0 9190

This theorem is referenced by: (None)