Theorem nfsab1 2795

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

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

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfsab1

Step	Hyp	Ref	Expression
1		hbab1 2794	. 2 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑})
2	1	nf5i 2192	1 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}

Syntax hints:  Ⅎwnf 1863   ∈ wcel 2158  {cab 2791

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1880  ax-4 1897  ax-5 2004  ax-6 2070  ax-7 2106  ax-10 2187  ax-12 2216

This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-ex 1860  df-nf 1865  df-sb 2063  df-clab 2792

This theorem is referenced by:  clelab  2931  nfab1  2949  ralab2  3566  rexab2  3568  eluniab  4637  elintab  4676  opabex3d  7372  opabex3  7373  setindtrs  38090  rababg  38376