Theorem pwne0 5312

Description: A power class is never empty. (Contributed by NM, 3-Sep-2018.)

Assertion

Ref	Expression
pwne0	⊢ 𝒫 𝐴 ≠ ∅

Proof of Theorem pwne0

Step	Hyp	Ref	Expression
1		0elpw 5311	. 2 ⊢ ∅ ∈ 𝒫 𝐴
2	1	ne0ii 4296	1 ⊢ 𝒫 𝐴 ≠ ∅

Syntax hints:   ≠ wne 2956  ∅c0 4285  𝒫 cpw 4554

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733  ax-nul 5255

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1562  df-fal 1572  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-ne 2957  df-v 3455  df-dif 3907  df-ss 3921  df-nul 4286  df-pw 4556

This theorem is referenced by:  undefne0  8255  afv20defat  47790