Theorem nfsab 2223

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 1567	. . 3 |- ( ph -> A. x ph )
3	2	hbab 2222	. 2 |- ( z e. { y | ph } -> A. x z e. { y | ph } )
4	3	nfi 1510	1 |- F/ x z e. { y | ph }

Syntax hints:   F/wnf 1508   e. wcel 2202   {cab 2217

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-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218

This theorem is referenced by:  nfab  2379  peano2  4693  lss1d  14396