Theorem nfsab1 2221

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 2220	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1510	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1508   e. wcel 2202   {cab 2217

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218

This theorem is referenced by:  abbi  2345  nfab1  2376  ralab2  2970  rexab2  2972  abn0m  3520  rabn0m  3522  eluniab  3905  elintab  3939  intexabim  4242  iinexgm  4244  opabex3d  6282  opabex3  6283