Theorem nfab1 2341

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

Assertion

Ref	Expression
nfab1	|- F/_ x { x | ph }

Proof of Theorem nfab1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfsab1 2186	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2329	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2182   F/_wnfc 2326

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-nfc 2328

This theorem is referenced by:  abid2f  2365  nfrab1  2677  elabgt  2905  elabgf  2906  nfsbc1d  3006  ss2ab  3252  abn0r  3476  euabsn  3693  iunab  3964  iinab  3979  iotaexab  5238  sniota  5250  nfixp1  6786  elabgft1  15508  elabgf2  15510