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

Theorem nfrel 5093
Description: Bound-variable hypothesis builder for a relation. (Contributed by NM, 31-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfrel.1
Assertion
Ref Expression
nfrel

Proof of Theorem nfrel
StepHypRef Expression
1 df-rel 5011 . 2
2 nfrel.1 . . 3
3 nfcv 2619 . . 3
42, 3nfss 3496 . 2
51, 4nfxfr 1645 1
Colors of variables: wff setvar class
Syntax hints:  F/wnf 1616  F/_wnfc 2605   cvv 3109  C_wss 3475  X.cxp 5002  Relwrel 5009
This theorem is referenced by:  nffun  5615
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-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-in 3482  df-ss 3489  df-rel 5011
  Copyright terms: Public domain W3C validator