ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfrel GIF version

Theorem nfrel 4511
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 4435 . 2 (Rel 𝐴𝐴 ⊆ (V × V))
2 nfrel.1 . . 3 𝑥𝐴
3 nfcv 2228 . . 3 𝑥(V × V)
42, 3nfss 3016 . 2 𝑥 𝐴 ⊆ (V × V)
51, 4nfxfr 1408 1 𝑥Rel 𝐴
Colors of variables: wff set class
Syntax hints:  wnf 1394  wnfc 2215  Vcvv 2619  wss 2997   × cxp 4426  Rel wrel 4433
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-in 3003  df-ss 3010  df-rel 4435
This theorem is referenced by:  nffun  5024
  Copyright terms: Public domain W3C validator