Theorem nfab1 2492

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

Assertion

Ref	Expression
nfab1	⊢ Ⅎx{x ∣ φ}

Proof of Theorem nfab1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfsab1 2343	. 2 ⊢ Ⅎx y ∈ {x ∣ φ}
2	1	nfci 2480	1 ⊢ Ⅎx{x ∣ φ}

Syntax hints:  {cab 2339  Ⅎwnfc 2477

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

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-nfc 2479

This theorem is referenced by:  nfabd2  2508  abid2f  2515  nfrab1  2792  elabgt  2983  elabgf  2984  nfsbc1d  3064  ss2ab  3335  abn0  3569  euabsn  3793  iunab  4013  iinab  4028  sniota  4370