Theorem nfsab1 2030

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 2029	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1351	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1349   e. wcel 1393   {cab 2026

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027

This theorem is referenced by:  abbi  2151  nfab1  2180  ralab2  2705  rexab2  2707  rabn0m  3245  eluniab  3592  elintab  3626  intexabim  3906  iinexgm  3908  opabex3d  5748  opabex3  5749