Theorem nfrn 4907

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	|- F/_ x A

Assertion

Ref	Expression
nfrn	|- F/_ x ran A

Proof of Theorem nfrn

Step	Hyp	Ref	Expression
1		df-rn 4670	. 2 |- ran A = dom `' A
2		nfrn.1	. . . 4 |- F/_ x A
3	2	nfcnv 4841	. . 3 |- F/_ x `' A
4	3	nfdm 4906	. 2 |- F/_ x dom `' A
5	1, 4	nfcxfr 2333	1 |- F/_ x ran A

Syntax hints:   F/_wnfc 2323   `'ccnv 4658   dom cdm 4659   ran crn 4660

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157  df-sn 3624  df-pr 3625  df-op 3627  df-br 4030  df-opab 4091  df-cnv 4667  df-dm 4669  df-rn 4670

This theorem is referenced by:  nfima  5013  nff  5400  nffo  5475  fliftfun  5839  nfseq  10528