Theorem nfsab1 2183

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 2182	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1473	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1471   e. wcel 2164   {cab 2179

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180

This theorem is referenced by:  abbi  2307  nfab1  2338  ralab2  2924  rexab2  2926  abn0m  3472  rabn0m  3474  eluniab  3847  elintab  3881  intexabim  4181  iinexgm  4183  opabex3d  6173  opabex3  6174