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Theorem an0r 109
Description: Conjunction with 0. (Contributed by NM, 26-Nov-1997.)
Assertion
Ref Expression
an0r (0 ∩ a) = 0

Proof of Theorem an0r
StepHypRef Expression
1 ancom 74 . 2 (0 ∩ a) = (a ∩ 0)
2 an0 108 . 2 (a ∩ 0) = 0
31, 2ax-r2 36 1 (0 ∩ a) = 0
Colors of variables: term
Syntax hints:   = wb 1  wa 7  0wf 9
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a4 33  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42
This theorem is referenced by:  ud3lem1a  566  ud3lem3b  573  ud5lem1b  587  ud5lem3a  591  ud5lem3b  592  bi3  839  bi4  840  mlaconj4  844  comanblem2  871  marsdenlem3  882  mhcor1  888  govar  896  lem3.3.7i3e1  1066
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