Theorem nfab1 2338

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 2183	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2326	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2179   F/_wnfc 2323

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-nfc 2325

This theorem is referenced by:  abid2f  2362  nfrab1  2674  elabgt  2901  elabgf  2902  nfsbc1d  3002  ss2ab  3247  abn0r  3471  euabsn  3688  iunab  3959  iinab  3974  iotaexab  5233  sniota  5245  nfixp1  6772  elabgft1  15270  elabgf2  15272