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Mirrors > Home > ILE Home > Th. List > 7nn0 | GIF version |
Description: 7 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
7nn0 | ⊢ 7 ∈ ℕ0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 7nn 9044 | . 2 ⊢ 7 ∈ ℕ | |
2 | 1 | nnnn0i 9143 | 1 ⊢ 7 ∈ ℕ0 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2141 7c7 8934 ℕ0cn0 9135 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-sep 4107 ax-cnex 7865 ax-resscn 7866 ax-1re 7868 ax-addrcl 7871 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-int 3832 df-br 3990 df-iota 5160 df-fv 5206 df-ov 5856 df-inn 8879 df-2 8937 df-3 8938 df-4 8939 df-5 8940 df-6 8941 df-7 8942 df-n0 9136 |
This theorem is referenced by: 7p4e11 9418 7p5e12 9419 7p6e13 9420 7p7e14 9421 8p8e16 9428 9p8e17 9435 9p9e18 9436 7t3e21 9452 7t4e28 9453 7t5e35 9454 7t6e42 9455 7t7e49 9456 8t8e64 9463 9t3e27 9465 9t4e36 9466 9t8e72 9470 9t9e81 9471 |
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