Theorem nfsab1 2222

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 2221	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1511	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1509   e. wcel 2203   {cab 2218

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-5 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219

This theorem is referenced by:  abbibcom  2346  abbib  2350  nfab1  2386  ralab2  2981  rexab2  2983  abn0m  3534  rabn0m  3536  eluniab  3926  elintab  3960  intexabim  4264  iinexgm  4266  opabex3d  6314  opabex3  6315