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Mirrors > Home > ILE Home > Th. List > omex | Unicode version |
Description: The existence of omega (the class of natural numbers). Axiom 7 of [TakeutiZaring] p. 43. (Contributed by NM, 6-Aug-1994.) |
Ref | Expression |
---|---|
omex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zfinf2 4255 |
. . 3
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2 | intexabim 3897 |
. . 3
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3 | 1, 2 | ax-mp 7 |
. 2
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4 | dfom3 4258 |
. . 3
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5 | 4 | eleq1i 2100 |
. 2
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6 | 3, 5 | mpbir 134 |
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 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-iinf 4254 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-v 2553 df-in 2918 df-ss 2925 df-int 3607 df-iom 4257 |
This theorem is referenced by: peano5 4264 omelon 4274 frecabex 5923 niex 6296 enq0ex 6422 nq0ex 6423 uzenom 8883 frecfzennn 8884 nnenom 8891 |
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