Theorem currysetALT 37383

Description: Alternate proof of curryset 37379, 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 2756	. 2 ⊢ {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)} = {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)}
2	1	currysetlem3 37382	1 ⊢ ¬ {𝑥 ∣ (𝑥 ∈ 𝑥 → 𝜑)} ∈ 𝑉

Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2136  {cab 2734

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-10 2169  ax-11 2185  ax-12 2206  ax-ext 2728  ax-sep 5240

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 857  df-tru 1557  df-ex 1794  df-nf 1798  df-sb 2085  df-clab 2735  df-cleq 2748  df-clel 2831  df-nfc 2905  df-v 3450

This theorem is referenced by: (None)