Theorem nfrab1 2792

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 2624	. 2 ⊢ {x ∈ A ∣ φ} = {x ∣ (x ∈ A ∧ φ)}
2		nfab1 2492	. 2 ⊢ Ⅎx{x ∣ (x ∈ A ∧ φ)}
3	1, 2	nfcxfr 2487	1 ⊢ Ⅎx{x ∈ A ∣ φ}

Syntax hints:   ∧ wa 358   ∈ wcel 1710  {cab 2339  Ⅎwnfc 2477  {crab 2619

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-rab 2624

This theorem is referenced by: (None)