Theorem nfab1 2377

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 2221	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2365	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2217   F/_wnfc 2362

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 1811  df-clab 2218  df-nfc 2364

This theorem is referenced by:  abid2f  2401  nfrab1  2714  elabgt  2948  elabgf  2949  nfsbc1d  3049  ss2ab  3296  abn0r  3521  euabsn  3745  iunab  4022  iinab  4037  iotaexab  5312  sniota  5324  nfixp1  6930  modom  7037  elabgft1  16479  elabgf2  16481