Theorem currysetALT 34283

Description: Alternate proof of curryset 34279, or more precisely alternate exposal of the same proof. (Contributed by BJ, 23-Sep-2023.) This proof is intuitionistically valid. (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
currysetALT	⊢ ¬ {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)} ∈ 𝑉

Distinct variable group:   𝜑,𝑥

Allowed substitution hint:   𝑉(𝑥)

Proof of Theorem currysetALT

Step	Hyp	Ref	Expression
1		eqid 2820	. 2 ⊢ {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)} = {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)}
2	1	currysetlem3 34282	1 ⊢ ¬ {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)} ∈ 𝑉

Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2113  {cab 2798

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2792  ax-sep 5196

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2799  df-cleq 2813  df-clel 2892  df-nfc 2962  df-v 3493

This theorem is referenced by: (None)