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Theorem fh2rc 480
 Description: Foulis-Holland Theorem.
Hypotheses
Ref Expression
fh.1 a C b
fh.2 a C c
Assertion
Ref Expression
fh2rc ((ca) ∩ b) = ((cb) ∪ (ab))

Proof of Theorem fh2rc
StepHypRef Expression
1 fh.1 . . 3 a C b
2 fh.2 . . 3 a C c
31, 2fh2r 474 . 2 ((ac) ∩ b) = ((ab) ∪ (cb))
4 ax-a2 31 . . 3 (ca) = (ac)
54ran 78 . 2 ((ca) ∩ b) = ((ac) ∩ b)
6 ax-a2 31 . 2 ((cb) ∪ (ab)) = ((ab) ∪ (cb))
73, 5, 63tr1 63 1 ((ca) ∩ b) = ((cb) ∪ (ab))
 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:  mlalem  832  bi3  839  bi4  840  mlaconj4  844  comanblem1  870  mhlem  876  mhlem1  877  marsdenlem2  881  cancellem  891
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