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Theorem pw1ne0 7146
 Description: The power set of 1o is not zero. (Contributed by Jim Kingdon, 30-Jul-2024.)
Assertion
Ref Expression
pw1ne0 𝒫 1o ≠ ∅

Proof of Theorem pw1ne0
StepHypRef Expression
1 0elpw 4124 . 2 ∅ ∈ 𝒫 1o
21ne0ii 3403 1 𝒫 1o ≠ ∅
 Colors of variables: wff set class Syntax hints:   ≠ wne 2327  ∅c0 3394  𝒫 cpw 3543  1oc1o 6350 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-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-nul 4090 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ne 2328  df-v 2714  df-dif 3104  df-in 3108  df-ss 3115  df-nul 3395  df-pw 3545 This theorem is referenced by:  pw1nel3  7149  sucpw1nel3  7151
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