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Mirrors > Home > ILE Home > Th. List > cbvreu | Unicode version |
Description: Change the bound variable of a restricted unique existential quantifier using implicit substitution. (Contributed by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
cbvral.1 |
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cbvral.2 |
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cbvral.3 |
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Ref | Expression |
---|---|
cbvreu |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1509 |
. . . 4
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2 | 1 | sb8eu 2013 |
. . 3
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3 | sban 1929 |
. . . 4
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4 | 3 | eubii 2009 |
. . 3
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5 | clelsb3 2245 |
. . . . . 6
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6 | 5 | anbi1i 454 |
. . . . 5
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7 | 6 | eubii 2009 |
. . . 4
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8 | nfv 1509 |
. . . . . 6
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9 | cbvral.1 |
. . . . . . 7
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10 | 9 | nfsb 1920 |
. . . . . 6
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11 | 8, 10 | nfan 1545 |
. . . . 5
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12 | nfv 1509 |
. . . . 5
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13 | eleq1 2203 |
. . . . . 6
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14 | sbequ 1813 |
. . . . . . 7
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15 | cbvral.2 |
. . . . . . . 8
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16 | cbvral.3 |
. . . . . . . 8
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17 | 15, 16 | sbie 1765 |
. . . . . . 7
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18 | 14, 17 | syl6bb 195 |
. . . . . 6
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19 | 13, 18 | anbi12d 465 |
. . . . 5
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20 | 11, 12, 19 | cbveu 2024 |
. . . 4
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21 | 7, 20 | bitri 183 |
. . 3
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22 | 2, 4, 21 | 3bitri 205 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | df-reu 2424 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | df-reu 2424 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 22, 23, 24 | 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 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-cleq 2133 df-clel 2136 df-reu 2424 |
This theorem is referenced by: cbvrmo 2656 cbvreuv 2659 |
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