Theorem nfab1 2284

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 2130	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2272	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2126   F/_wnfc 2269

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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-nfc 2271

This theorem is referenced by:  abid2f  2307  nfrab1  2613  elabgt  2829  elabgf  2830  nfsbc1d  2929  ss2ab  3170  abn0r  3392  euabsn  3601  iunab  3867  iinab  3882  sniota  5123  nfixp1  6620  elabgft1  13156  elabgf2  13158