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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 4370 | . 2 ⊢ (Rel 𝐴 ↔ 𝐴 ⊆ (V × V)) | |
2 | nfrel.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | nfcv 2219 | . . 3 ⊢ Ⅎ𝑥(V × V) | |
4 | 2, 3 | nfss 2992 | . 2 ⊢ Ⅎ𝑥 𝐴 ⊆ (V × V) |
5 | 1, 4 | nfxfr 1403 | 1 ⊢ Ⅎ𝑥Rel 𝐴 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1389 Ⅎwnfc 2206 Vcvv 2601 ⊆ wss 2973 × cxp 4361 Rel wrel 4368 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-in 2979 df-ss 2986 df-rel 4370 |
This theorem is referenced by: nffun 4944 |
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