Theorem nfab1 2374

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 2219	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2362	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2215   F/_wnfc 2359

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-nfc 2361

This theorem is referenced by:  abid2f  2398  nfrab1  2711  elabgt  2945  elabgf  2946  nfsbc1d  3046  ss2ab  3293  abn0r  3517  euabsn  3739  iunab  4015  iinab  4030  iotaexab  5303  sniota  5315  nfixp1  6882  modom  6989  elabgft1  16310  elabgf2  16312