Theorem nfab1 2231

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 2079	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2219	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2075   F/_wnfc 2216

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473

This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-nfc 2218

This theorem is referenced by:  abid2f  2254  nfrab1  2547  elabgt  2758  elabgf  2759  nfsbc1d  2857  ss2ab  3090  abn0r  3311  euabsn  3516  iunab  3782  iinab  3797  sniota  5020  nfixp1  6489  elabgft1  11951  elabgf2  11953