Theorem nfab1 2321

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 2167	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2309	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2163   F/_wnfc 2306

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-nfc 2308

This theorem is referenced by:  abid2f  2345  nfrab1  2657  elabgt  2879  elabgf  2880  nfsbc1d  2980  ss2ab  3224  abn0r  3448  euabsn  3663  iunab  3934  iinab  3949  sniota  5208  nfixp1  6718  elabgft1  14533  elabgf2  14535