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Mirrors > Home > NFE Home > Th. List > ax11v2 | Unicode version |
Description: Recovery of ax-11o 2141 from ax11v 2096. This proof uses ax-10 2140 and ax-11 1746. TODO: figure out if this is useful, or if it should be simplified or eliminated. (Contributed by NM, 2-Feb-2007.) |
Ref | Expression |
---|---|
ax11v2.1 |
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Ref | Expression |
---|---|
ax11v2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9ev 1656 |
. 2
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2 | ax11v2.1 |
. . . . 5
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3 | equequ2 1686 |
. . . . . . 7
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4 | 3 | adantl 452 |
. . . . . 6
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5 | dveeq2 1940 |
. . . . . . . . 9
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6 | 5 | imp 418 |
. . . . . . . 8
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7 | nfa1 1788 |
. . . . . . . . 9
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8 | 3 | imbi1d 308 |
. . . . . . . . . 10
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9 | 8 | sps 1754 |
. . . . . . . . 9
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10 | 7, 9 | albid 1772 |
. . . . . . . 8
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11 | 6, 10 | syl 15 |
. . . . . . 7
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12 | 11 | imbi2d 307 |
. . . . . 6
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13 | 4, 12 | imbi12d 311 |
. . . . 5
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14 | 2, 13 | mpbii 202 |
. . . 4
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15 | 14 | ex 423 |
. . 3
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16 | 15 | exlimdv 1636 |
. 2
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17 | 1, 16 | mpi 16 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: ax11a2 1993 |
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