Theorem nfab1 2349

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 2194	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2337	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2190   F/_wnfc 2334

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-11 1528  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-clab 2191  df-nfc 2336

This theorem is referenced by:  abid2f  2373  nfrab1  2685  elabgt  2913  elabgf  2914  nfsbc1d  3014  ss2ab  3260  abn0r  3484  euabsn  3702  iunab  3973  iinab  3988  iotaexab  5249  sniota  5261  nfixp1  6804  elabgft1  15676  elabgf2  15678