Theorem nfab1 2301

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 2147	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2289	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2143   F/_wnfc 2286

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-nfc 2288

This theorem is referenced by:  abid2f  2325  nfrab1  2636  elabgt  2853  elabgf  2854  nfsbc1d  2953  ss2ab  3196  abn0r  3418  euabsn  3629  iunab  3895  iinab  3910  sniota  5161  nfixp1  6660  elabgft1  13339  elabgf2  13341