Theorem nfrn 5025

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 4783	. 2 |- ran A = dom `' A
2		nfrn.1	. . . 4 |- F/_ x A
3	2	nfcnv 4957	. . 3 |- F/_ x `' A
4	3	nfdm 5024	. 2 |- F/_ x dom `' A
5	1, 4	nfcxfr 2389	1 |- F/_ x ran A

Syntax hints:   F/_wnfc 2379   `'ccnv 4771   dom cdm 4772   ran crn 4773

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-un 3224  df-sn 3714  df-pr 3715  df-op 3717  df-br 4129  df-opab 4191  df-cnv 4780  df-dm 4782  df-rn 4783

This theorem is referenced by:  nfima  5132  nff  5528  nffo  5612  fliftfun  5996  nfseq  10877