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Theorem nn0xnn0d 9061
Description: A standard nonnegative integer is an extended nonnegative integer, deduction form. (Contributed by AV, 10-Dec-2020.)
Hypothesis
Ref Expression
nn0xnn0d.1 (𝜑𝐴 ∈ ℕ0)
Assertion
Ref Expression
nn0xnn0d (𝜑𝐴 ∈ ℕ0*)

Proof of Theorem nn0xnn0d
StepHypRef Expression
1 nn0ssxnn0 9055 . 2 0 ⊆ ℕ0*
2 nn0xnn0d.1 . 2 (𝜑𝐴 ∈ ℕ0)
31, 2sseldi 3095 1 (𝜑𝐴 ∈ ℕ0*)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1480  0cn0 8989  0*cxnn0 9052
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-xnn0 9053
This theorem is referenced by: (None)
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