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Mathbox for Richard Penner |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > rp-fakeinunass | Structured version Visualization version Unicode version |
Description: A special case where a mixture of intersection and union appears to conform to a mixed associative law. (Contributed by Richard Penner, 26-Feb-2020.) |
Ref | Expression |
---|---|
rp-fakeinunass |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rp-fakeanorass 36169 |
. . 3
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2 | 1 | albii 1693 |
. 2
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3 | dfss2 3423 |
. 2
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4 | dfcleq 2447 |
. . 3
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5 | elun 3576 |
. . . . . 6
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6 | elin 3619 |
. . . . . . 7
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7 | 6 | orbi1i 523 |
. . . . . 6
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8 | 5, 7 | bitri 253 |
. . . . 5
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9 | elin 3619 |
. . . . . 6
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10 | elun 3576 |
. . . . . . 7
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11 | 10 | anbi2i 701 |
. . . . . 6
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12 | 9, 11 | bitri 253 |
. . . . 5
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13 | 8, 12 | bibi12i 317 |
. . . 4
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14 | 13 | albii 1693 |
. . 3
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15 | 4, 14 | bitri 253 |
. 2
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16 | 2, 3, 15 | 3bitr4i 281 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-v 3049 df-un 3411 df-in 3413 df-ss 3420 |
This theorem is referenced by: rp-fakeuninass 36173 |
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