Theorem currysetlem2

Description: Lemma for currysetALT . (Contributed by BJ, 23-Sep-2023) This proof is intuitionistically valid. (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	currysetlem2.def	⊢ 𝑋 = { 𝑥 ∣ ( 𝑥 ∈ 𝑥 → 𝜑 ) }
Assertion	currysetlem2	⊢ ( 𝑋 ∈ 𝑉 → ( 𝑋 ∈ 𝑋 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		currysetlem2.def	⊢ 𝑋 = { 𝑥 ∣ ( 𝑥 ∈ 𝑥 → 𝜑 ) }
2	1	currysetlem1	⊢ ( 𝑋 ∈ 𝑉 → ( 𝑋 ∈ 𝑋 ↔ ( 𝑋 ∈ 𝑋 → 𝜑 ) ) )
3	2	biimpd	⊢ ( 𝑋 ∈ 𝑉 → ( 𝑋 ∈ 𝑋 → ( 𝑋 ∈ 𝑋 → 𝜑 ) ) )
4	3	pm2.43d	⊢ ( 𝑋 ∈ 𝑉 → ( 𝑋 ∈ 𝑋 → 𝜑 ) )