Theorem nfab1 2374

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 2219	. 2 |- F/ x y e. { x | ph }
2	1	nfci 2362	1 |- F/_ x { x | ph }

Syntax hints:   {cab 2215   F/_wnfc 2359

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-nfc 2361

This theorem is referenced by:  abid2f  2398  nfrab1  2711  elabgt  2944  elabgf  2945  nfsbc1d  3045  ss2ab  3292  abn0r  3516  euabsn  3736  iunab  4011  iinab  4026  iotaexab  5296  sniota  5308  nfixp1  6863  elabgft1  16100  elabgf2  16102