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Description: Distributive law for conjunction. Theorem *4.4 of [WhiteheadRussell] p. 118. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 5-Jan-2013.) |
Ref | Expression |
---|---|
andi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 713 |
. . 3
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2 | olc 712 |
. . 3
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3 | 1, 2 | jaodan 798 |
. 2
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4 | orc 713 |
. . . 4
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5 | 4 | anim2i 342 |
. . 3
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6 | olc 712 |
. . . 4
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7 | 6 | anim2i 342 |
. . 3
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8 | 5, 7 | jaoi 717 |
. 2
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9 | 3, 8 | impbii 126 |
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 710 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: andir 820 anddi 822 dcim 842 excxor 1389 sbequilem 1849 sborv 1902 r19.43 2648 indi 3397 difindiss 3404 unrab 3421 unipr 3838 uniun 3843 unopab 4097 xpundi 4700 coundir 5149 unpreima 5662 tpostpos 6289 elni2 7343 elznn0nn 9297 |
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