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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdsepnft | Unicode version |
Description: Closed form of bdsepnf 13257. Version of ax-bdsep 13253 with one disjoint variable condition removed, the other disjoint variable condition replaced by a non-freeness antecedent, and without initial universal quantifier. Use bdsep1 13254 when sufficient. (Contributed by BJ, 19-Oct-2019.) |
Ref | Expression |
---|---|
bdsepnft.1 |
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Ref | Expression |
---|---|
bdsepnft |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdsepnft.1 |
. . 3
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2 | 1 | bdsep2 13255 |
. 2
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3 | nfnf1 1524 |
. . . 4
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4 | 3 | nfal 1556 |
. . 3
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5 | nfa1 1522 |
. . . 4
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6 | nfvd 1510 |
. . . . 5
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7 | nfv 1509 |
. . . . . . 7
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8 | 7 | a1i 9 |
. . . . . 6
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9 | sp 1489 |
. . . . . 6
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10 | 8, 9 | nfand 1548 |
. . . . 5
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11 | 6, 10 | nfbid 1568 |
. . . 4
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12 | 5, 11 | nfald 1734 |
. . 3
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13 | nfv 1509 |
. . . . . 6
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14 | 5, 13 | nfan 1545 |
. . . . 5
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15 | elequ2 1692 |
. . . . . . 7
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16 | 15 | adantl 275 |
. . . . . 6
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17 | 16 | bibi1d 232 |
. . . . 5
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18 | 14, 17 | albid 1595 |
. . . 4
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19 | 18 | ex 114 |
. . 3
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20 | 4, 12, 19 | cbvexd 1900 |
. 2
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21 | 2, 20 | mpbii 147 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-bdsep 13253 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-cleq 2133 df-clel 2136 |
This theorem is referenced by: bdsepnf 13257 |
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