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Mirrors > Home > MPE Home > Th. List > intmin4 | Structured version Visualization version Unicode version |
Description: Elimination of a conjunct in a class intersection. (Contributed by NM, 31-Jul-2006.) |
Ref | Expression |
---|---|
intmin4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssintab 4265 |
. . . 4
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2 | simpr 467 |
. . . . . . . 8
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3 | ancr 556 |
. . . . . . . 8
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4 | 2, 3 | impbid2 209 |
. . . . . . 7
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5 | 4 | imbi1d 323 |
. . . . . 6
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6 | 5 | alimi 1695 |
. . . . 5
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7 | albi 1701 |
. . . . 5
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8 | 6, 7 | syl 17 |
. . . 4
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9 | 1, 8 | sylbi 200 |
. . 3
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10 | vex 3060 |
. . . 4
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11 | 10 | elintab 4259 |
. . 3
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12 | 10 | elintab 4259 |
. . 3
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13 | 9, 11, 12 | 3bitr4g 296 |
. 2
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14 | 13 | eqrdv 2460 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ral 2754 df-v 3059 df-in 3423 df-ss 3430 df-int 4249 |
This theorem is referenced by: (None) |
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