Theorem currysetALT 34385

Description: Alternate proof of curryset 34381, 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 2798	. 2 ⊢ {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)} = {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)}
2	1	currysetlem3 34384	1 ⊢ ¬ {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)} ∈ 𝑉

Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2111  {cab 2776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5167

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-v 3443

This theorem is referenced by: (None)