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Mirrors > Home > ILE Home > Th. List > niex | GIF version |
Description: The class of positive integers is a set. (Contributed by NM, 15-Aug-1995.) |
Ref | Expression |
---|---|
niex | ⊢ N ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omex 4336 | . 2 ⊢ ω ∈ V | |
2 | df-ni 6545 | . . 3 ⊢ N = (ω ∖ {∅}) | |
3 | difss 3099 | . . 3 ⊢ (ω ∖ {∅}) ⊆ ω | |
4 | 2, 3 | eqsstri 3030 | . 2 ⊢ N ⊆ ω |
5 | 1, 4 | ssexi 3918 | 1 ⊢ N ∈ V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1434 Vcvv 2602 ∖ cdif 2971 ∅c0 3252 {csn 3400 ωcom 4333 Ncnpi 6513 |
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 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 ax-sep 3898 ax-iinf 4331 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-ral 2354 df-v 2604 df-dif 2976 df-in 2980 df-ss 2987 df-int 3639 df-iom 4334 df-ni 6545 |
This theorem is referenced by: enqex 6601 nqex 6604 enq0ex 6680 nq0ex 6681 |
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