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Mirrors > Home > MPE Home > Th. List > rintn0 | Structured version Visualization version Unicode version |
Description: Relative intersection of a nonempty set. (Contributed by Stefan O'Rear, 3-Apr-2015.) (Revised by Mario Carneiro, 5-Jun-2015.) |
Ref | Expression |
---|---|
rintn0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | incom 3624 |
. 2
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2 | intssuni2 4259 |
. . . 4
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3 | ssid 3450 |
. . . . 5
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4 | sspwuni 4366 |
. . . . 5
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5 | 3, 4 | mpbi 212 |
. . . 4
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6 | 2, 5 | syl6ss 3443 |
. . 3
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7 | df-ss 3417 |
. . 3
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8 | 6, 7 | sylib 200 |
. 2
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9 | 1, 8 | syl5eq 2496 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-v 3046 df-dif 3406 df-in 3410 df-ss 3417 df-nul 3731 df-pw 3952 df-uni 4198 df-int 4234 |
This theorem is referenced by: mrerintcl 15496 ismred2 15502 |
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