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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 4649 | . 2 ⊢ ran 𝐴 = dom ◡𝐴 | |
2 | nfrn.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfcnv 4818 | . . 3 ⊢ Ⅎ𝑥◡𝐴 |
4 | 3 | nfdm 4883 | . 2 ⊢ Ⅎ𝑥dom ◡𝐴 |
5 | 1, 4 | nfcxfr 2326 | 1 ⊢ Ⅎ𝑥ran 𝐴 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnfc 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 |
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