Theorem nfab1 2352

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 2197	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2340	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2193   F/_wnfc 2337

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-nfc 2339

This theorem is referenced by:  abid2f  2376  nfrab1  2688  elabgt  2921  elabgf  2922  nfsbc1d  3022  ss2ab  3269  abn0r  3493  euabsn  3713  iunab  3988  iinab  4003  iotaexab  5269  sniota  5281  nfixp1  6828  elabgft1  15914  elabgf2  15916