Theorem nfrab1 2483

Description: The abstraction variable in a restricted class abstraction isn't free. (Contributed by NM, 19-Mar-1997.)

Assertion

Ref	Expression
nfrab1	⊢ Ⅎx{x ∈ A ∣ φ}

Proof of Theorem nfrab1

Step	Hyp	Ref	Expression
1		df-rab 2309	. 2 ⊢ {x ∈ A ∣ φ} = {x ∣ (x ∈ A ∧ φ)}
2		nfab1 2177	. 2 ⊢ Ⅎx{x ∣ (x ∈ A ∧ φ)}
3	1, 2	nfcxfr 2172	1 ⊢ Ⅎx{x ∈ A ∣ φ}

Syntax hints:   ∧ wa 97   ∈ wcel 1390  {cab 2023  Ⅎwnfc 2162  {crab 2304

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309

This theorem is referenced by:  repizf2  3906  rabxfrd  4167  tfis  4249  fvmptssdm  5198