MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfsab1 Structured version   Unicode version

Theorem nfsab1 2451
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
StepHypRef Expression
1 hbab1 2450 . 2  |-  ( y  e.  { x  | 
ph }  ->  A. x  y  e.  { x  |  ph } )
21nfi 1601 1  |-  F/ x  y  e.  { x  |  ph }
Colors of variables: wff setvar class
Syntax hints:   F/wnf 1594    e. wcel 1762   {cab 2447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-12 1798  ax-13 1963
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2448
This theorem is referenced by:  abbiOLD  2594  clelab  2606  nfab1  2626  ralab2  3263  rexab2  3265  eluniab  4251  elintab  4288  opabex3d  6754  opabex3  6755  setindtrs  30562
  Copyright terms: Public domain W3C validator