Theorem pwidgOLD 4579

Description: Obsolete version of pwidg 4578 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 3961	. 2 ⊢ 𝐴 ⊆ 𝐴
2		elpwg 4561	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 ∈ 𝒫 𝐴 ↔ 𝐴 ⊆ 𝐴))
3	1, 2	mpbiri 261	1 ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ 𝒫 𝐴)

Syntax hints:   → wi 4   ∈ wcel 2145   ⊆ wss 3907  𝒫 cpw 4558

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1566  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-ss 3924  df-pw 4560

This theorem is referenced by: (None)