Theorem pwidgOLD 4570

Description: Obsolete version of pwidg 4569 as of 10-Jun-2026. (Contributed by Stefan O'Rear, 1-Feb-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
pwidgOLD	⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ 𝒫 𝐴)

Proof of Theorem pwidgOLD

Step	Hyp	Ref	Expression
1		ssid 3953	. 2 ⊢ 𝐴 ⊆ 𝐴
2		elpwg 4552	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 ∈ 𝒫 𝐴 ↔ 𝐴 ⊆ 𝐴))
3	1, 2	mpbiri 260	1 ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ 𝒫 𝐴)

Syntax hints:   → wi 4   ∈ wcel 2136   ⊆ wss 3899  𝒫 cpw 4549

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1809  ax-4 1823  ax-5 1924  ax-6 1981  ax-7 2022  ax-8 2138  ax-9 2146  ax-ext 2728

This theorem depends on definitions:  df-bi 209  df-an 399  df-tru 1557  df-ex 1794  df-sb 2085  df-clab 2735  df-cleq 2748  df-clel 2831  df-ss 3916  df-pw 4551

This theorem is referenced by: (None)