Theorem nfsab1 2228

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 2227	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1515	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1513   e. wcel 2209   {cab 2224

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225

This theorem is referenced by:  abbibcom  2352  abbib  2356  nfab1  2394  ralab2  2990  rexab2  2992  abn0m  3547  rabn0m  3549  eluniab  3942  elintab  3976  intexabim  4283  iinexgm  4285  opabex3d  6340  opabex3  6341