Theorem pwidgOLD 4581

Description: Obsolete version of pwidg 4580 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 3956	. 2 ⊢ 𝐴 ⊆ 𝐴
2		elpwg 4563	. 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 ∈ 𝒫 𝐴 ↔ 𝐴 ⊆ 𝐴))
3	1, 2	mpbiri 261	1 ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ 𝒫 𝐴)

This proof depends on syntax axioms:   → wi 4   ∈ wcel 2145   ⊆ wss 3902  𝒫 cpw 4560

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-ss 3919  df-pw 4562

This theorem is used by: (None)