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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 669 |
. . 3
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2 | olc 668 |
. . 3
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3 | 1, 2 | jaodan 747 |
. 2
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4 | orc 669 |
. . . 4
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5 | 4 | anim2i 335 |
. . 3
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6 | olc 668 |
. . . 4
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7 | 6 | anim2i 335 |
. . 3
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8 | 5, 7 | jaoi 672 |
. 2
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9 | 3, 8 | impbii 125 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: andir 769 anddi 771 dcim 823 dcan 881 excxor 1315 sbequilem 1767 sborv 1819 r19.43 2526 indi 3247 difindiss 3254 unrab 3271 unipr 3673 uniun 3678 unopab 3923 xpundi 4507 coundir 4946 unpreima 5438 tpostpos 6043 elni2 6934 elznn0nn 8825 |
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