Theorem nfsab1 2394

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 2393	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1557	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1550   e. wcel 1721   {cab 2390

This theorem is referenced by:  abbi  2514  nfab1  2542  ralab2  3059  rexab2  3061  eluniab  3987  elintab  4021  opabex3d  5948  opabex3  5949  setindtrs  26986

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946

This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391