Theorem bj-nfsab1 37560

Description: Remove dependency on ax-13 2401 from nfsab1 2746. UPDATE / TODO: nfsab1 2746 does not use ax-13 2401 either anymore; bj-nfsab1 37560 is shorter than nfsab1 2746 but uses ax-12 2213. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-nfsab1	⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥, 𝑦)

Proof of Theorem bj-nfsab1

Step	Hyp	Ref	Expression
1		hbab1 2747	. 2 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑})
2	1	nf5i 2183	1 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}

This proof depends on syntax axioms:  Ⅎwnf 1816   ∈ wcel 2145  {cab 2738

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-10 2178  ax-12 2213

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-ex 1813  df-nf 1817  df-sb 2100  df-clab 2739

This theorem is used by: (None)