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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | andi 807 | . 2 | |
2 | ancom 264 | . 2 | |
3 | ancom 264 | . . 3 | |
4 | ancom 264 | . . 3 | |
5 | 3, 4 | orbi12i 753 | . 2 |
6 | 1, 2, 5 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wo 697 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: anddi 810 dcan 918 excxor 1356 xordc1 1371 sbequilem 1810 rexun 3256 rabun2 3355 reuun2 3359 xpundir 4596 coundi 5040 mptun 5254 tpostpos 6161 ltxr 9562 |
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