Theorem nfsab1 2155

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 2154	. 2 |- ( y e. { x | ph } -> A. x y e. { x | ph } )
2	1	nfi 1450	1 |- F/ x y e. { x | ph }

Syntax hints:   F/wnf 1448   e. wcel 2136   {cab 2151

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-11 1494  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-clab 2152

This theorem is referenced by:  abbi  2280  nfab1  2310  ralab2  2890  rexab2  2892  abn0m  3434  rabn0m  3436  eluniab  3801  elintab  3835  intexabim  4131  iinexgm  4133  opabex3d  6089  opabex3  6090