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Mirrors > Home > ILE Home > Th. List > nfcnv | GIF version |
Description: Bound-variable hypothesis builder for converse. (Contributed by NM, 31-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfcnv.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfcnv | ⊢ Ⅎ𝑥◡𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-cnv 4547 | . 2 ⊢ ◡𝐴 = {〈𝑦, 𝑧〉 ∣ 𝑧𝐴𝑦} | |
2 | nfcv 2281 | . . . 4 ⊢ Ⅎ𝑥𝑧 | |
3 | nfcnv.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
4 | nfcv 2281 | . . . 4 ⊢ Ⅎ𝑥𝑦 | |
5 | 2, 3, 4 | nfbr 3974 | . . 3 ⊢ Ⅎ𝑥 𝑧𝐴𝑦 |
6 | 5 | nfopab 3996 | . 2 ⊢ Ⅎ𝑥{〈𝑦, 𝑧〉 ∣ 𝑧𝐴𝑦} |
7 | 1, 6 | nfcxfr 2278 | 1 ⊢ Ⅎ𝑥◡𝐴 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnfc 2268 class class class wbr 3929 {copab 3988 ◡ccnv 4538 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-cnv 4547 |
This theorem is referenced by: nfrn 4784 nffun 5146 nff1 5326 nfinf 6904 |
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