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Theorem 7nn0 9157
Description: 7 is a nonnegative integer. (Contributed by Mario Carneiro, 19-Apr-2015.)
Assertion
Ref Expression
7nn0 7 ∈ ℕ0

Proof of Theorem 7nn0
StepHypRef Expression
1 7nn 9044 . 2 7 ∈ ℕ
21nnnn0i 9143 1 7 ∈ ℕ0
Colors of variables: wff set class
Syntax hints:  wcel 2141  7c7 8934  0cn0 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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