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Theorem nnne0s 28341
Description: A surreal positive integer is non-zero. (Contributed by Scott Fenton, 15-Apr-2025.)
Assertion
Ref Expression
nnne0s (𝐴 ∈ ℕs𝐴 ≠ 0s )

Proof of Theorem nnne0s
StepHypRef Expression
1 eldifsni 4789 . 2 (𝐴 ∈ (ℕ0s ∖ { 0s }) → 𝐴 ≠ 0s )
2 df-nns 28322 . 2 s = (ℕ0s ∖ { 0s })
31, 2eleq2s 2858 1 (𝐴 ∈ ℕs𝐴 ≠ 0s )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  wne 2939  cdif 3947  {csn 4625   0s c0s 27868  0scnn0s 28319  scnns 28320
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-ne 2940  df-v 3481  df-dif 3953  df-sn 4626  df-nns 28322
This theorem is referenced by:  nnsgt0  28343  2ne0s  28405  expsnnval  28410  recut  28429  0reno  28430  renegscl  28431  readdscl  28432  remulscllem1  28433  remulscl  28435
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