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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 8030 |
. . . . 5
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2 | 1 | neli 2457 |
. . . 4
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3 | nn0re 9216 |
. . . 4
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4 | 2, 3 | mto 663 |
. . 3
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5 | eleq1 2252 |
. . 3
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6 | 4, 5 | mtbiri 676 |
. 2
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7 | 6 | necon2ai 2414 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-un 4451 ax-cnex 7933 ax-resscn 7934 ax-1re 7936 ax-addrcl 7939 ax-rnegex 7951 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-nel 2456 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-uni 3825 df-int 3860 df-pnf 8025 df-inn 8951 df-n0 9208 |
This theorem is referenced by: nn0nepnfd 9280 fxnn0nninf 10471 0tonninf 10472 1tonninf 10473 |
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