MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfaba1 Structured version   Unicode version

Theorem nfaba1 2621
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 14-Oct-2016.)
Assertion
Ref Expression
nfaba1  |-  F/_ x { y  |  A. x ph }

Proof of Theorem nfaba1
StepHypRef Expression
1 nfa1 1902 . 2  |-  F/ x A. x ph
21nfab 2620 1  |-  F/_ x { y  |  A. x ph }
Colors of variables: wff setvar class
Syntax hints:   A.wal 1396   {cab 2439   F/_wnfc 2602
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-nfc 2604
This theorem is referenced by:  nfopd  4220  nfimad  5334  nfiota1  5536  nffvd  5857
  Copyright terms: Public domain W3C validator