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Theorem mh2 884
 Description: Marsden-Herman distributive law. Corollary 3.3 of Beran, p. 259.
Hypotheses
Ref Expression
marsden.1 a C b
marsden.2 b C c
marsden.3 c C d
marsden.4 d C a
Assertion
Ref Expression
mh2 ((ab) ∩ (cd)) = (((ac) ∪ (ad)) ∪ ((bc) ∪ (bd)))

Proof of Theorem mh2
StepHypRef Expression
1 marsden.1 . 2 a C b
2 marsden.4 . . 3 d C a
32comcom 453 . 2 a C d
4 marsden.2 . . 3 b C c
54comcom 453 . 2 c C b
6 marsden.3 . 2 c C d
71, 3, 5, 6mh 879 1 ((ab) ∩ (cd)) = (((ac) ∪ (ad)) ∪ ((bc) ∪ (bd)))
 Colors of variables: term Syntax hints:   = wb 1   C wc 3   ∪ wo 6   ∩ wa 7 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  mhcor1  888
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