Theorem nfsab1 2046

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 2045	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1367	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1365   e. wcel 1409   {cab 2042

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443

This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043

This theorem is referenced by:  abbi  2167  nfab1  2196  ralab2  2727  rexab2  2729  rabn0m  3272  eluniab  3619  elintab  3653  intexabim  3933  iinexgm  3935  opabex3d  5775  opabex3  5776