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

Theorem nfrel 5114
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 𝑥𝐴
Assertion
Ref Expression
nfrel 𝑥Rel 𝐴

Proof of Theorem nfrel
StepHypRef Expression
1 df-rel 5032 . 2 (Rel 𝐴𝐴 ⊆ (V × V))
2 nfrel.1 . . 3 𝑥𝐴
3 nfcv 2747 . . 3 𝑥(V × V)
42, 3nfss 3557 . 2 𝑥 𝐴 ⊆ (V × V)
51, 4nfxfr 1770 1 𝑥Rel 𝐴
Colors of variables: wff setvar class
Syntax hints:  wnf 1698  wnfc 2734  Vcvv 3169  wss 3536   × cxp 5023  Rel wrel 5030
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2032  ax-13 2229  ax-ext 2586
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2593  df-cleq 2599  df-clel 2602  df-nfc 2736  df-ral 2897  df-in 3543  df-ss 3550  df-rel 5032
This theorem is referenced by:  nffun  5809
  Copyright terms: Public domain W3C validator