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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 1539 |
. . . . 5
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2 | 1 | sb8 1867 |
. . . 4
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3 | sbbi 1971 |
. . . . . 6
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4 | sb8eu.1 |
. . . . . . . 8
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5 | 4 | nfsb 1958 |
. . . . . . 7
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6 | equsb3 1963 |
. . . . . . . 8
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7 | nfv 1539 |
. . . . . . . 8
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8 | 6, 7 | nfxfr 1485 |
. . . . . . 7
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9 | 5, 8 | nfbi 1600 |
. . . . . 6
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10 | 3, 9 | nfxfr 1485 |
. . . . 5
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11 | nfv 1539 |
. . . . 5
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12 | sbequ 1851 |
. . . . 5
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13 | 10, 11, 12 | cbval 1765 |
. . . 4
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14 | equsb3 1963 |
. . . . . 6
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15 | 14 | sblbis 1972 |
. . . . 5
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16 | 15 | albii 1481 |
. . . 4
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17 | 2, 13, 16 | 3bitri 206 |
. . 3
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18 | 17 | exbii 1616 |
. 2
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19 | df-eu 2041 |
. 2
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20 | df-eu 2041 |
. 2
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21 | 18, 19, 20 | 3bitr4i 212 |
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 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 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 |
This theorem is referenced by: sb8mo 2052 nfeud 2054 nfeu 2057 cbveu 2062 cbvreu 2716 acexmid 5891 |
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