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Mirrors > Home > ILE Home > Th. List > nfrel | GIF version |
Description: Bound-variable hypothesis builder for a relation. (Contributed by NM, 31-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfrel.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfrel | ⊢ Ⅎ𝑥Rel 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rel 4352 | . 2 ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V)) | |
2 | nfrel.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | nfcv 2178 | . . 3 ⊢ Ⅎ𝑥(V × V) | |
4 | 2, 3 | nfss 2938 | . 2 ⊢ Ⅎ𝑥 𝐴 ⊆ (V × V) |
5 | 1, 4 | nfxfr 1363 | 1 ⊢ Ⅎ𝑥Rel 𝐴 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1349 Ⅎwnfc 2165 Vcvv 2557 ⊆ wss 2917 × cxp 4343 Rel wrel 4350 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-in 2924 df-ss 2931 df-rel 4352 |
This theorem is referenced by: nffun 4924 |
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