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Mirrors > Home > ILE 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 818 |
. 2
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2 | ancom 266 |
. 2
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3 | ancom 266 |
. . 3
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4 | ancom 266 |
. . 3
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5 | 3, 4 | orbi12i 764 |
. 2
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6 | 1, 2, 5 | 3bitr4i 212 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: anddi 821 dcan 933 excxor 1378 xordc1 1393 sbequilem 1838 rexun 3316 rabun2 3415 reuun2 3419 xpundir 4684 coundi 5131 mptun 5348 tpostpos 6265 ltxr 9775 pythagtriplem2 12266 pythagtrip 12283 |
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