Theorem nfab1 2350

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 2195	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2338	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2191   F/_wnfc 2335

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-nfc 2337

This theorem is referenced by:  abid2f  2374  nfrab1  2686  elabgt  2914  elabgf  2915  nfsbc1d  3015  ss2ab  3261  abn0r  3485  euabsn  3703  iunab  3974  iinab  3989  iotaexab  5250  sniota  5262  nfixp1  6805  elabgft1  15714  elabgf2  15716