Theorem nfsab1 2071

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 2070	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1391	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1389   e. wcel 1433   {cab 2067

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068

This theorem is referenced by:  abbi  2192  nfab1  2221  ralab2  2756  rexab2  2758  rabn0m  3272  eluniab  3613  elintab  3647  intexabim  3927  iinexgm  3929  opabex3d  5768  opabex3  5769