Theorem nfsab1 2167

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 2166	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1462	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1460   e. wcel 2148   {cab 2163

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164

This theorem is referenced by:  abbi  2291  nfab1  2321  ralab2  2903  rexab2  2905  abn0m  3450  rabn0m  3452  eluniab  3823  elintab  3857  intexabim  4154  iinexgm  4156  opabex3d  6124  opabex3  6125