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Mirrors > Home > NFE Home > Th. List > pm2.61dne | Unicode version |
Description: Deduction eliminating an inequality in an antecedent. (Contributed by NM, 1-Jun-2007.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
pm2.61dne.1 |
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pm2.61dne.2 |
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Ref | Expression |
---|---|
pm2.61dne |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61dne.2 |
. 2
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2 | nne 2521 |
. . 3
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3 | pm2.61dne.1 |
. . 3
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4 | 2, 3 | syl5bi 208 |
. 2
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5 | 1, 4 | pm2.61d 150 |
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-ne 2519 |
This theorem is referenced by: pm2.61dane 2595 |
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