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Mirrors > Home > NFE Home > Th. List > ax12olem3 | Unicode version |
Description: Lemma for ax12o 1934. Show the equivalence of an intermediate equivalent to ax12o 1934 with the conjunction of ax-12 1925 and a variant with negated equalities. (Contributed by NM, 24-Dec-2015.) |
Ref | Expression |
---|---|
ax12olem3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 1747 |
. . . . . 6
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2 | 1 | con2i 112 |
. . . . 5
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3 | 2 | imim1i 54 |
. . . 4
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4 | 3 | imim2i 13 |
. . 3
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5 | sp 1747 |
. . . . . 6
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6 | 5 | imim2i 13 |
. . . . 5
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7 | 6 | con1d 116 |
. . . 4
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8 | 7 | imim2i 13 |
. . 3
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9 | 4, 8 | jca 518 |
. 2
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10 | con1 120 |
. . . . . 6
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11 | 10 | imim1d 69 |
. . . . 5
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12 | 11 | com12 27 |
. . . 4
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13 | 12 | imim3i 55 |
. . 3
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14 | 13 | imp 418 |
. 2
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15 | 9, 14 | impbii 180 |
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-11 1746 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 |
This theorem is referenced by: ax12olem4 1930 |
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