Theorem nfsab1 2194

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfsab1	|- F/ x y e. { x | ph }

Distinct variable group:   x, y

Allowed substitution hints:   ph( x, y)

Proof of Theorem nfsab1

Step	Hyp	Ref	Expression
1		hbab1 2193	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1484	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1482   e. wcel 2175   {cab 2190

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-11 1528  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-clab 2191

This theorem is referenced by:  abbi  2318  nfab1  2349  ralab2  2936  rexab2  2938  abn0m  3485  rabn0m  3487  eluniab  3861  elintab  3895  intexabim  4195  iinexgm  4197  opabex3d  6205  opabex3  6206