Theorem nfsab1 2197

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 2196	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1486	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1484   e. wcel 2178   {cab 2193

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194

This theorem is referenced by:  abbi  2321  nfab1  2352  ralab2  2944  rexab2  2946  abn0m  3494  rabn0m  3496  eluniab  3876  elintab  3910  intexabim  4212  iinexgm  4214  opabex3d  6229  opabex3  6230