Theorem nfsab1 2129

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 2128	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1438	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1436   e. wcel 1480   {cab 2125

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126

This theorem is referenced by:  abbi  2253  nfab1  2283  ralab2  2848  rexab2  2850  abn0m  3388  rabn0m  3390  eluniab  3748  elintab  3782  intexabim  4077  iinexgm  4079  opabex3d  6019  opabex3  6020