Theorem nfab1 2386

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 2222	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2374	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2218   F/_wnfc 2371

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 2219  df-nfc 2373

This theorem is referenced by:  abid2f  2410  nfrab1  2724  elabgt  2958  elabgf  2959  nfsbc1d  3059  ss2ab  3306  abn0r  3533  euabsn  3761  iunab  4038  iinab  4053  iotaexab  5331  sniota  5343  nfixp1  6953  modom  7061  elabgft1  16550  elabgf2  16552