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

Theorem nfrn 4884
Description: Bound-variable hypothesis builder for range. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypothesis
Ref Expression
nfrn.1 𝑥𝐴
Assertion
Ref Expression
nfrn 𝑥ran 𝐴

Proof of Theorem nfrn
StepHypRef Expression
1 df-rn 4649 . 2 ran 𝐴 = dom 𝐴
2 nfrn.1 . . . 4 𝑥𝐴
32nfcnv 4818 . . 3 𝑥𝐴
43nfdm 4883 . 2 𝑥dom 𝐴
51, 4nfcxfr 2326 1 𝑥ran 𝐴
Colors of variables: wff set class
Syntax hints:  wnfc 2316  ccnv 4637  dom cdm 4638  ran crn 4639
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-3an 981  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-un 3145  df-sn 3610  df-pr 3611  df-op 3613  df-br 4016  df-opab 4077  df-cnv 4646  df-dm 4648  df-rn 4649
This theorem is referenced by:  nfima  4990  nff  5374  nffo  5449  fliftfun  5810  nfseq  10468
  Copyright terms: Public domain W3C validator