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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > rexdifpr | Structured version Visualization version Unicode version |
Description: Restricted existential quantification over a set with two elements removed. (Contributed by Alexander van der Vekens, 7-Feb-2018.) |
Ref | Expression |
---|---|
rexdifpr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldifpr 3992 |
. . . . 5
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2 | 3anass 990 |
. . . . 5
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3 | 1, 2 | bitri 253 |
. . . 4
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4 | 3 | anbi1i 702 |
. . 3
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5 | anass 655 |
. . . 4
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6 | df-3an 988 |
. . . . . 6
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7 | 6 | bicomi 206 |
. . . . 5
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8 | 7 | anbi2i 701 |
. . . 4
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9 | 5, 8 | bitri 253 |
. . 3
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10 | 4, 9 | bitri 253 |
. 2
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11 | 10 | rexbii2 2889 |
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-3an 988 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-ne 2626 df-rex 2745 df-v 3049 df-dif 3409 df-un 3411 df-sn 3971 df-pr 3973 |
This theorem is referenced by: usgra2pth0 39773 |
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