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Mirrors > Home > MPE Home > Th. List > ceqsalt | Structured version Visualization version Unicode version |
Description: Closed theorem version of ceqsalg 3040. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsalt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 3025 |
. . . 4
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2 | 1 | 3ad2ant3 1032 |
. . 3
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3 | biimp 198 |
. . . . . . 7
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4 | 3 | imim3i 61 |
. . . . . 6
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5 | 4 | al2imi 1691 |
. . . . 5
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6 | 5 | 3ad2ant2 1031 |
. . . 4
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7 | 19.23t 1996 |
. . . . 5
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8 | 7 | 3ad2ant1 1030 |
. . . 4
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9 | 6, 8 | sylibd 222 |
. . 3
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10 | 2, 9 | mpid 42 |
. 2
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11 | biimpr 203 |
. . . . . . 7
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12 | 11 | imim2i 16 |
. . . . . 6
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13 | 12 | com23 81 |
. . . . 5
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14 | 13 | alimi 1688 |
. . . 4
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15 | 14 | 3ad2ant2 1031 |
. . 3
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16 | 19.21t 1991 |
. . . 4
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17 | 16 | 3ad2ant1 1030 |
. . 3
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18 | 15, 17 | mpbid 215 |
. 2
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19 | 10, 18 | impbid 195 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-10 1919 ax-12 1937 ax-ext 2432 |
This theorem depends on definitions: df-bi 190 df-an 377 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-clab 2439 df-cleq 2445 df-clel 2448 df-v 3015 |
This theorem is referenced by: ceqsralt 3039 ceqsalg 3040 |
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