Theorem nfsab 2181

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 1530	. . 3 |- ( ph -> A. x ph )
3	2	hbab 2180	. 2 |- ( z e. { y | ph } -> A. x z e. { y | ph } )
4	3	nfi 1473	1 |- F/ x z e. { y | ph }

Syntax hints:   F/wnf 1471   e. wcel 2160   {cab 2175

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176

This theorem is referenced by:  nfab  2337  peano2  4612  lss1d  13699