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Mirrors > Home > MPE Home > Th. List > ax12olem3OLD | Unicode version |
Description: Obsolete proof of ax12oOLD 1984 as of 30-Jan-2018. Lemma for ax12oOLD 1984. Show the equivalence of an intermediate equivalent to ax12o 1976 with the conjunction of ax-12 1946 and a variant with negated equalities. (Contributed by NM, 24-Dec-2015.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
ax12olem3OLD |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 1759 |
. . . . . 6
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2 | 1 | con2i 114 |
. . . . 5
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3 | 2 | imim1i 56 |
. . . 4
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4 | 3 | imim2i 14 |
. . 3
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5 | sp 1759 |
. . . . . 6
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6 | 5 | imim2i 14 |
. . . . 5
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7 | 6 | con1d 118 |
. . . 4
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8 | 7 | imim2i 14 |
. . 3
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9 | 4, 8 | jca 519 |
. 2
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10 | con1 122 |
. . . . . 6
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11 | 10 | imim1d 71 |
. . . . 5
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12 | 11 | com12 29 |
. . . 4
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13 | 12 | imim3i 57 |
. . 3
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14 | 13 | imp 419 |
. 2
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15 | 9, 14 | impbii 181 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: ax12olem4OLD 1980 ax12olem4wAUX7 29164 ax12olem4OLD7 29391 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-11 1757 |
This theorem depends on definitions: df-bi 178 df-an 361 df-ex 1548 |
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