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Mirrors > Home > ILE Home > Th. List > nffrfor | Unicode 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 |
---|---|
nffrfor.r |
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nffrfor.a |
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nffrfor.s |
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Ref | Expression |
---|---|
nffrfor |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-frfor 4182 |
. 2
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2 | nffrfor.a |
. . . 4
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3 | nfcv 2235 |
. . . . . . . 8
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4 | nffrfor.r |
. . . . . . . 8
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5 | nfcv 2235 |
. . . . . . . 8
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6 | 3, 4, 5 | nfbr 3911 |
. . . . . . 7
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7 | nffrfor.s |
. . . . . . . 8
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8 | 7 | nfcri 2229 |
. . . . . . 7
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9 | 6, 8 | nfim 1516 |
. . . . . 6
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10 | 2, 9 | nfralxy 2425 |
. . . . 5
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11 | 7 | nfcri 2229 |
. . . . 5
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12 | 10, 11 | nfim 1516 |
. . . 4
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13 | 2, 12 | nfralxy 2425 |
. . 3
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14 | 2, 7 | nfss 3032 |
. . 3
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15 | 13, 14 | nfim 1516 |
. 2
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16 | 1, 15 | nfxfr 1415 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-v 2635 df-un 3017 df-in 3019 df-ss 3026 df-sn 3472 df-pr 3473 df-op 3475 df-br 3868 df-frfor 4182 |
This theorem is referenced by: nffr 4200 |
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