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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 4350 | . 2 ⊢ (𝑅 Fr 𝐴 ↔ ∀𝑠 FrFor 𝑅𝐴𝑠) | |
2 | nffr.r | . . . 4 ⊢ Ⅎ𝑥𝑅 | |
3 | nffr.a | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
4 | nfcv 2332 | . . . 4 ⊢ Ⅎ𝑥𝑠 | |
5 | 2, 3, 4 | nffrfor 4366 | . . 3 ⊢ Ⅎ𝑥 FrFor 𝑅𝐴𝑠 |
6 | 5 | nfal 1587 | . 2 ⊢ Ⅎ𝑥∀𝑠 FrFor 𝑅𝐴𝑠 |
7 | 1, 6 | nfxfr 1485 | 1 ⊢ Ⅎ𝑥 𝑅 Fr 𝐴 |
Colors of variables: wff set class |
Syntax hints: ∀wal 1362 Ⅎwnf 1471 Ⅎwnfc 2319 FrFor wfrfor 4345 Fr wfr 4346 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-frfor 4349 df-frind 4350 |
This theorem is referenced by: nfwe 4373 |
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