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Mirrors > Home > ILE Home > Th. List > ax11v2 | Unicode version |
Description: Recovery of ax11o 1833 from ax11v 1838 without using ax-11 1517. The hypothesis
is even weaker than ax11v 1838, with ![]() ![]() ![]() |
Ref | Expression |
---|---|
ax11v2.1 |
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Ref | Expression |
---|---|
ax11v2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1707 |
. 2
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2 | ax11v2.1 |
. . . . 5
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3 | equequ2 1724 |
. . . . . . 7
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4 | 3 | adantl 277 |
. . . . . 6
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5 | dveeq2 1826 |
. . . . . . . . 9
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6 | 5 | imp 124 |
. . . . . . . 8
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7 | hba1 1551 |
. . . . . . . . 9
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8 | 3 | imbi1d 231 |
. . . . . . . . . 10
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9 | 8 | sps 1548 |
. . . . . . . . 9
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10 | 7, 9 | albidh 1491 |
. . . . . . . 8
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11 | 6, 10 | syl 14 |
. . . . . . 7
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12 | 11 | imbi2d 230 |
. . . . . 6
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13 | 4, 12 | imbi12d 234 |
. . . . 5
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14 | 2, 13 | mpbii 148 |
. . . 4
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15 | 14 | ex 115 |
. . 3
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16 | 15 | exlimdv 1830 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 1, 16 | mpi 15 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-in2 616 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-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: ax11a2 1832 |
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