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Theorem pw1ne0 7274
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 4189 . 2 ∅ ∈ 𝒫 1o
21ne0ii 3452 1 𝒫 1o ≠ ∅
Colors of variables: wff set class
Syntax hints:  wne 2360  c0 3442  𝒫 cpw 3597  1oc1o 6449
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-nul 4151
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ne 2361  df-v 2758  df-dif 3151  df-in 3155  df-ss 3162  df-nul 3443  df-pw 3599
This theorem is referenced by:  pw1nel3  7277  sucpw1nel3  7279
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