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Mirrors > Home > NFE Home > Th. List > ax16i | Unicode version |
Description: Inference with ax16 2045 as its conclusion. (Contributed by NM, 20-May-2008.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
ax16i.1 |
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ax16i.2 |
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Ref | Expression |
---|---|
ax16i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() | |
2 | nfv 1619 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() | |
3 | ax-8 1675 |
. . 3
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4 | 1, 2, 3 | cbv3 1982 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | ax-8 1675 |
. . . . 5
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6 | 5 | spimv 1990 |
. . . 4
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7 | equcomi 1679 |
. . . . . 6
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8 | equcomi 1679 |
. . . . . . 7
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9 | ax-8 1675 |
. . . . . . 7
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10 | 8, 9 | syl 15 |
. . . . . 6
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11 | 7, 10 | syl5com 26 |
. . . . 5
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12 | 11 | alimdv 1621 |
. . . 4
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13 | 6, 12 | mpcom 32 |
. . 3
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14 | equcomi 1679 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 14 | alimi 1559 |
. . 3
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16 | 13, 15 | syl 15 |
. 2
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17 | ax16i.1 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 17 | biimpcd 215 |
. . . 4
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19 | 18 | alimdv 1621 |
. . 3
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20 | ax16i.2 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 20 | nfi 1551 |
. . . 4
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22 | nfv 1619 |
. . . 4
![]() ![]() ![]() ![]() | |
23 | 17 | biimprd 214 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 14, 23 | syl 15 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 21, 22, 24 | cbv3 1982 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 19, 25 | syl6com 31 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 4, 16, 26 | 3syl 18 |
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: ax16ALT 2047 |
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