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Mirrors > Home > ILE Home > Th. List > nffr | GIF version |
Description: Bound-variable hypothesis builder for well-founded relations. (Contributed by Stefan O'Rear, 20-Jan-2015.) (Revised by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
nffr.r | ⊢ Ⅎ𝑥𝑅 |
nffr.a | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nffr | ⊢ Ⅎ𝑥 𝑅 Fr 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-frind 4157 | . 2 ⊢ (𝑅 Fr 𝐴 ↔ ∀𝑠 FrFor 𝑅𝐴𝑠) | |
2 | nffr.r | . . . 4 ⊢ Ⅎ𝑥𝑅 | |
3 | nffr.a | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
4 | nfcv 2228 | . . . 4 ⊢ Ⅎ𝑥𝑠 | |
5 | 2, 3, 4 | nffrfor 4173 | . . 3 ⊢ Ⅎ𝑥 FrFor 𝑅𝐴𝑠 |
6 | 5 | nfal 1513 | . 2 ⊢ Ⅎ𝑥∀𝑠 FrFor 𝑅𝐴𝑠 |
7 | 1, 6 | nfxfr 1408 | 1 ⊢ Ⅎ𝑥 𝑅 Fr 𝐴 |
Colors of variables: wff set class |
Syntax hints: ∀wal 1287 Ⅎwnf 1394 Ⅎwnfc 2215 FrFor wfrfor 4152 Fr wfr 4153 |
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 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-sn 3450 df-pr 3451 df-op 3453 df-br 3844 df-frfor 4156 df-frind 4157 |
This theorem is referenced by: nfwe 4180 |
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