Theorem nfab1 2388

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 2224	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2376	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2220   F/_wnfc 2373

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-nfc 2375

This theorem is referenced by:  abid2f  2412  nfrab1  2726  elabgt  2961  elabgf  2962  nfsbc1d  3062  ss2ab  3310  abn0r  3537  euabsn  3766  iunab  4043  iinab  4058  iotaexab  5336  sniota  5348  nfixp1  6966  modom  7074  elabgft1  16676  elabgf2  16678