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Mirrors > Home > ILE Home > Th. List > nfrn | GIF version |
Description: Bound-variable hypothesis builder for range. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfrn.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfrn | ⊢ Ⅎ𝑥ran 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rn 4510 | . 2 ⊢ ran 𝐴 = dom ◡𝐴 | |
2 | nfrn.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfcnv 4678 | . . 3 ⊢ Ⅎ𝑥◡𝐴 |
4 | 3 | nfdm 4743 | . 2 ⊢ Ⅎ𝑥dom ◡𝐴 |
5 | 1, 4 | nfcxfr 2252 | 1 ⊢ Ⅎ𝑥ran 𝐴 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnfc 2242 ◡ccnv 4498 dom cdm 4499 ran crn 4500 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-un 3041 df-sn 3499 df-pr 3500 df-op 3502 df-br 3896 df-opab 3950 df-cnv 4507 df-dm 4509 df-rn 4510 |
This theorem is referenced by: nfima 4847 nff 5227 nffo 5302 fliftfun 5651 nfseq 10121 |
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