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Mirrors > Home > MPE Home > Th. List > eeeanv | Structured version Visualization version Unicode version |
Description: Rearrange existential quantifiers. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.) Reduce distinct variable restrictions. (Revised by Wolf Lammen, 20-Jan-2018.) |
Ref | Expression |
---|---|
eeeanv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eeanv 2078 |
. . 3
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2 | 1 | anbi1i 701 |
. 2
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3 | df-3an 987 |
. . . . . 6
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4 | 3 | exbii 1718 |
. . . . 5
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5 | 19.42v 1834 |
. . . . 5
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6 | 4, 5 | bitri 253 |
. . . 4
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7 | 6 | 2exbii 1719 |
. . 3
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8 | nfv 1761 |
. . . . . 6
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9 | 8 | nfex 2031 |
. . . . 5
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10 | 9 | 19.41 2051 |
. . . 4
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11 | 10 | exbii 1718 |
. . 3
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12 | nfv 1761 |
. . . . 5
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13 | 12 | nfex 2031 |
. . . 4
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14 | 13 | 19.41 2051 |
. . 3
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15 | 7, 11, 14 | 3bitri 275 |
. 2
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16 | df-3an 987 |
. 2
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17 | 2, 15, 16 | 3bitr4i 281 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 |
This theorem depends on definitions: df-bi 189 df-an 373 df-3an 987 df-ex 1664 df-nf 1668 |
This theorem is referenced by: vtocl3 3103 spc3egv 3138 eloprabga 6383 |
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