MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfab1 Structured version   Unicode version

Theorem nfab1 2573
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
nfab1  |-  F/_ x { x  |  ph }

Proof of Theorem nfab1
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 nfsab1 2425 . 2  |-  F/ x  y  e.  { x  |  ph }
21nfci 2561 1  |-  F/_ x { x  |  ph }
Colors of variables: wff set class
Syntax hints:   {cab 2421   F/_wnfc 2558
This theorem is referenced by:  nfabd2  2589  abid2f  2596  nfrab1  2880  elabgt  3071  elabgf  3072  nfsbc1d  3170  ss2ab  3403  abn0  3638  euabsn  3868  iunab  4129  iinab  4144  zfrep4  4320  sniota  5437  opabiotafun  6528  nfriota1  6549  nfixp1  7074  scottexs  7803  scott0s  7804  cp  7807  ofpreima  24073  qqhval2  24358  sigaclcu2  24495  compab  27611  bnj1366  29138  bnj1321  29333  bnj1384  29338
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-nfc 2560
  Copyright terms: Public domain W3C validator