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Mirrors > Home > NFE Home > Th. List > pm2.61da3ne | Unicode version |
Description: Deduction eliminating three inequalities in an antecedent. (Contributed by NM, 15-Jun-2013.) |
Ref | Expression |
---|---|
pm2.61da3ne.1 |
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pm2.61da3ne.2 |
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pm2.61da3ne.3 |
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pm2.61da3ne.4 |
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Ref | Expression |
---|---|
pm2.61da3ne |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61da3ne.1 |
. 2
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2 | pm2.61da3ne.2 |
. 2
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3 | pm2.61da3ne.3 |
. . . 4
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4 | 3 | adantlr 695 |
. . 3
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5 | simpll 730 |
. . . 4
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6 | simplrl 736 |
. . . 4
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7 | simplrr 737 |
. . . 4
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8 | simpr 447 |
. . . 4
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9 | pm2.61da3ne.4 |
. . . 4
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10 | 5, 6, 7, 8, 9 | syl13anc 1184 |
. . 3
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11 | 4, 10 | pm2.61dane 2595 |
. 2
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12 | 1, 2, 11 | pm2.61da2ne 2596 |
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 |
This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936 df-ne 2519 |
This theorem is referenced by: (None) |
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