Theorem nfab1 2283

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 2129	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2271	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2125   F/_wnfc 2268

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-nfc 2270

This theorem is referenced by:  abid2f  2306  nfrab1  2610  elabgt  2825  elabgf  2826  nfsbc1d  2925  ss2ab  3165  abn0r  3387  euabsn  3593  iunab  3859  iinab  3874  sniota  5115  nfixp1  6612  elabgft1  12985  elabgf2  12987