Theorem nfsab 2157

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfsab.1	|- F/ x ph

Assertion

Ref	Expression
nfsab	|- F/ x z e. { y | ph }

Distinct variable group:   x, z

Allowed substitution hints:   ph( x, y, z)

Proof of Theorem nfsab

Step	Hyp	Ref	Expression
1		nfsab.1	. . . 4 |- F/ x ph
2	1	nfri 1507	. . 3 |- ( ph -> A. x ph )
3	2	hbab 2156	. 2 |- ( z e. { y | ph } -> A. x z e. { y | ph } )
4	3	nfi 1450	1 |- F/ x z e. { y | ph }

Syntax hints:   F/wnf 1448   e. wcel 2136   {cab 2151

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-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-clab 2152

This theorem is referenced by:  nfab  2313  peano2  4572