Theorem nfsab1 2426

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 2425	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1560	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1553   e. wcel 1725   {cab 2422

This theorem is referenced by:  abbi  2546  nfab1  2574  ralab2  3099  rexab2  3101  eluniab  4027  elintab  4061  opabex3d  5989  opabex3  5990  setindtrs  27096

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950

This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423