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Theorem oa4ctob 967
Description: Derivation of 4-OA law variant. (Contributed by NM, 22-Dec-1998.)
Hypothesis
Ref Expression
oa4ctob.1 (a ∩ (a ∪ (c ∩ (((ac) ∪ ((a1 g) ∩ (c1 g))) ∪ (((ae) ∪ ((a1 g) ∩ (e1 g))) ∩ ((ce) ∪ ((c1 g) ∩ (e1 g)))))))) ≤ g
Assertion
Ref Expression
oa4ctob ((a1 g) ∩ (a ∪ (c ∩ (((ac) ∪ ((a1 g) ∩ (c1 g))) ∪ (((ae) ∪ ((a1 g) ∩ (e1 g))) ∩ ((ce) ∪ ((c1 g) ∩ (e1 g)))))))) ≤ g

Proof of Theorem oa4ctob
StepHypRef Expression
1 oa4ctob.1 . 2 (a ∩ (a ∪ (c ∩ (((ac) ∪ ((a1 g) ∩ (c1 g))) ∪ (((ae) ∪ ((a1 g) ∩ (e1 g))) ∩ ((ce) ∪ ((c1 g) ∩ (e1 g)))))))) ≤ g
21oas 925 1 ((a1 g) ∩ (a ∪ (c ∩ (((ac) ∪ ((a1 g) ∩ (c1 g))) ∪ (((ae) ∪ ((a1 g) ∩ (e1 g))) ∩ ((ce) ∪ ((c1 g) ∩ (e1 g)))))))) ≤ g
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:  axoa4b  1035
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