Theorem nfsab1 2186

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 2185	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1476	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1474   e. wcel 2167   {cab 2182

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183

This theorem is referenced by:  abbi  2310  nfab1  2341  ralab2  2928  rexab2  2930  abn0m  3476  rabn0m  3478  eluniab  3851  elintab  3885  intexabim  4185  iinexgm  4187  opabex3d  6178  opabex3  6179