Theorem nfsab1 2219

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 2218	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1508	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1506   e. wcel 2200   {cab 2215

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

This theorem is referenced by:  abbi  2343  nfab1  2374  ralab2  2967  rexab2  2969  abn0m  3517  rabn0m  3519  eluniab  3899  elintab  3933  intexabim  4235  iinexgm  4237  opabex3d  6264  opabex3  6265