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

Theorem nfse 4859
 Description: Bound-variable hypothesis builder for set-like relations. (Contributed by Mario Carneiro, 24-Jun-2015.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nffr.r
nffr.a
Assertion
Ref Expression
nfse

Proof of Theorem nfse
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-se 4844 . 2
2 nffr.a . . 3
3 nfcv 2619 . . . . . 6
4 nffr.r . . . . . 6
5 nfcv 2619 . . . . . 6
63, 4, 5nfbr 4496 . . . . 5
76, 2nfrab 3039 . . . 4
87nfel1 2635 . . 3
92, 8nfral 2843 . 2
101, 9nfxfr 1645 1
 Colors of variables: wff setvar class Syntax hints:  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  A.wral 2807  {crab 2811   cvv 3109   class class class wbr 4452  Sewse 4841 This theorem is referenced by:  nfoi  7960 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-se 4844
 Copyright terms: Public domain W3C validator