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Mirrors > Home > ILE Home > Th. List > sb8eu | Unicode version |
Description: Variable substitution in unique existential quantifier. (Contributed by NM, 7-Aug-1994.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
sb8eu.1 |
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Ref | Expression |
---|---|
sb8eu |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1509 |
. . . . 5
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2 | 1 | sb8 1829 |
. . . 4
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3 | sbbi 1933 |
. . . . . 6
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4 | sb8eu.1 |
. . . . . . . 8
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5 | 4 | nfsb 1920 |
. . . . . . 7
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6 | equsb3 1925 |
. . . . . . . 8
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7 | nfv 1509 |
. . . . . . . 8
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8 | 6, 7 | nfxfr 1451 |
. . . . . . 7
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9 | 5, 8 | nfbi 1569 |
. . . . . 6
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10 | 3, 9 | nfxfr 1451 |
. . . . 5
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11 | nfv 1509 |
. . . . 5
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12 | sbequ 1813 |
. . . . 5
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13 | 10, 11, 12 | cbval 1728 |
. . . 4
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14 | equsb3 1925 |
. . . . . 6
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15 | 14 | sblbis 1934 |
. . . . 5
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16 | 15 | albii 1447 |
. . . 4
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17 | 2, 13, 16 | 3bitri 205 |
. . 3
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18 | 17 | exbii 1585 |
. 2
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19 | df-eu 2003 |
. 2
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20 | df-eu 2003 |
. 2
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21 | 18, 19, 20 | 3bitr4i 211 |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 |
This theorem is referenced by: sb8mo 2014 nfeud 2016 nfeu 2019 cbveu 2024 cbvreu 2655 acexmid 5781 |
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