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Mirrors > Home > ILE Home > Th. List > ax11ev | Unicode version |
Description: Analogue to ax11v 1827 for existential quantification. (Contributed by Jim Kingdon, 9-Jan-2018.) |
Ref | Expression |
---|---|
ax11ev |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1696 |
. 2
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2 | ax11e 1796 |
. . . . 5
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3 | ax-17 1526 |
. . . . . 6
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4 | 3 | 19.9h 1643 |
. . . . 5
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5 | 2, 4 | imbitrdi 161 |
. . . 4
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6 | equequ2 1713 |
. . . . 5
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7 | 6 | anbi1d 465 |
. . . . . . 7
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8 | 7 | exbidv 1825 |
. . . . . 6
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9 | 8 | imbi1d 231 |
. . . . 5
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10 | 6, 9 | imbi12d 234 |
. . . 4
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11 | 5, 10 | mpbii 148 |
. . 3
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12 | 11 | exlimiv 1598 |
. 2
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13 | 1, 12 | ax-mp 5 |
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-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: (None) |
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