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Mirrors > Home > ILE Home > Th. List > nn0nepnf | Unicode version |
Description: No standard nonnegative integer equals positive infinity. (Contributed by AV, 10-Dec-2020.) |
Ref | Expression |
---|---|
nn0nepnf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pnfnre 7450 |
. . . . 5
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2 | 1 | neli 2348 |
. . . 4
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3 | nn0re 8592 |
. . . 4
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4 | 2, 3 | mto 621 |
. . 3
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5 | eleq1 2147 |
. . 3
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6 | 4, 5 | mtbiri 633 |
. 2
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7 | 6 | necon2ai 2305 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-13 1447 ax-14 1448 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 ax-sep 3925 ax-un 4227 ax-cnex 7357 ax-resscn 7358 ax-1re 7360 ax-addrcl 7363 ax-rnegex 7375 |
This theorem depends on definitions: df-bi 115 df-tru 1290 df-fal 1293 df-nf 1393 df-sb 1690 df-clab 2072 df-cleq 2078 df-clel 2081 df-nfc 2214 df-ne 2252 df-nel 2347 df-ral 2360 df-rex 2361 df-rab 2364 df-v 2616 df-un 2990 df-in 2992 df-ss 2999 df-pw 3411 df-sn 3431 df-uni 3631 df-int 3666 df-pnf 7445 df-inn 8335 df-n0 8584 |
This theorem is referenced by: nn0nepnfd 8656 fxnn0nninf 9747 0tonninf 9748 1tonninf 9749 |
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