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Mirrors > Home > NFE Home > Th. List > ax12olem6 | Unicode version |
Description: Lemma for ax12o 1934. Derivation of ax12o 1934 from the hypotheses, without using ax12o 1934. (Contributed by Andrew Salmon, 21-Jul-2011.) (Revised by NM, 24-Dec-2015.) |
Ref | Expression |
---|---|
ax12olem6.1 |
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ax12olem6.2 |
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Ref | Expression |
---|---|
ax12olem6 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbn1 1730 |
. . . . 5
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2 | ax12olem6.1 |
. . . . 5
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3 | 1, 2 | hbim1 1810 |
. . . 4
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4 | ax-17 1616 |
. . . 4
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5 | equcom 1680 |
. . . . . 6
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6 | equequ1 1684 |
. . . . . 6
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7 | 5, 6 | syl5bb 248 |
. . . . 5
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8 | 7 | imbi2d 307 |
. . . 4
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9 | ax12olem6.2 |
. . . 4
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10 | 3, 4, 8, 9 | dvelimhw 1849 |
. . 3
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11 | 1 | 19.21h 1797 |
. . 3
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12 | 10, 11 | syl6ib 217 |
. 2
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13 | 12 | pm2.86d 93 |
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 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-nf 1545 |
This theorem is referenced by: ax12olem7 1933 |
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