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Theorem oa3-2wto2 989
 Description: Derivation of 3-OA variant from weaker version. (Contributed by NM, 25-Dec-1998.)
Hypothesis
Ref Expression
oa3-2wto2.1 (a ∩ (a ∪ (b ∩ ((ab) ∪ ((a1 c) ∩ (b1 c)))))) ≤ c
Assertion
Ref Expression
oa3-2wto2 ((a1 c) ∩ (a ∪ (b ∩ ((ab) ∪ ((a1 c) ∩ (b1 c)))))) ≤ c

Proof of Theorem oa3-2wto2
StepHypRef Expression
1 oa3-2wto2.1 . 2 (a ∩ (a ∪ (b ∩ ((ab) ∪ ((a1 c) ∩ (b1 c)))))) ≤ c
21oas 925 1 ((a1 c) ∩ (a ∪ (b ∩ ((ab) ∪ ((a1 c) ∩ (b1 c)))))) ≤ c
 Colors of variables: term Syntax hints:   ≤ wle 2  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →1 wi1 12 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-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by: (None)
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