Theorem nfsab1 2072

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 2071	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1392	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1390   e. wcel 1434   {cab 2068

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069

This theorem is referenced by:  abbi  2193  nfab1  2222  ralab2  2757  rexab2  2759  rabn0m  3273  eluniab  3615  elintab  3649  intexabim  3929  iinexgm  3931  opabex3d  5773  opabex3  5774