Theorem nfsab1 2160

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 2159	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1455	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1453   e. wcel 2141   {cab 2156

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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157

This theorem is referenced by:  abbi  2284  nfab1  2314  ralab2  2894  rexab2  2896  abn0m  3440  rabn0m  3442  eluniab  3808  elintab  3842  intexabim  4138  iinexgm  4140  opabex3d  6100  opabex3  6101