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Mirrors > Home > NFE Home > Th. List > andir | Unicode version |
Description: Distributive law for conjunction. (Contributed by NM, 12-Aug-1994.) |
Ref | Expression |
---|---|
andir |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | andi 837 |
. 2
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2 | ancom 437 |
. 2
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3 | ancom 437 |
. . 3
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4 | ancom 437 |
. . 3
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5 | 3, 4 | orbi12i 507 |
. 2
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6 | 1, 2, 5 | 3bitr4i 268 |
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 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 |
This theorem is referenced by: anddi 840 cador 1391 rexun 3443 rabun2 3534 reuun2 3538 elimif 3691 xpundir 4833 coundi 5082 nchoicelem18 6306 |
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