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Theorem 3vth3 806
Description: A 3-variable theorem. Equivalent to OML. (Contributed by NM, 18-Oct-1998.)
Assertion
Ref Expression
3vth3 ((a2 c) ∪ ((a2 b) ∩ (bc) )) = (a2 c)

Proof of Theorem 3vth3
StepHypRef Expression
1 ax-a2 31 . 2 ((a2 c) ∪ ((a2 b) ∩ (bc) )) = (((a2 b) ∩ (bc) ) ∪ (a2 c))
2 3vth1 804 . . 3 ((a2 b) ∩ (bc) ) ≤ (a2 c)
32df-le2 131 . 2 (((a2 b) ∩ (bc) ) ∪ (a2 c)) = (a2 c)
41, 3ax-r2 36 1 ((a2 c) ∪ ((a2 b) ∩ (bc) )) = (a2 c)
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  wa 7  2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  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-i2 45  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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