Theorem nfsab1 2085

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 2084	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1403	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1401   e. wcel 1445   {cab 2081

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-11 1449  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479

This theorem depends on definitions:  df-bi 116  df-nf 1402  df-sb 1700  df-clab 2082

This theorem is referenced by:  abbi  2208  nfab1  2237  ralab2  2793  rexab2  2795  abn0m  3327  rabn0m  3329  eluniab  3687  elintab  3721  intexabim  4009  iinexgm  4011  opabex3d  5930  opabex3  5931