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Theorem andi 837
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.)
Assertion
Ref Expression
andi

Proof of Theorem andi
StepHypRef Expression
1 orc 374 . . 3
2 olc 373 . . 3
31, 2jaodan 760 . 2
4 orc 374 . . . 4
54anim2i 552 . . 3
6 olc 373 . . . 4
76anim2i 552 . . 3
85, 7jaoi 368 . 2
93, 8impbii 180 1
Colors of variables: wff setvar class
Syntax hints:   wb 176   wo 357   wa 358
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:  andir  838  anddi  840  indi  3501  indifdir  3511  unrab  3526  unipr  3905  uniun  3910  unopab  4638  xpundi  4832  coundir  5083  imadif  5171  unpreima  5408  nmembers1lem3  6270
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