Theorem nfsab1 2612

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 2611	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nf5i 2024	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1708   e. wcel 1990   {cab 2608

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609

This theorem is referenced by:  clelab  2748  nfab1  2766  ralab2  3371  rexab2  3373  eluniab  4447  elintab  4487  opabex3d  7145  opabex3  7146  setindtrs  37592  rababg  37879