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Theorem orbile 843
 Description: Disjunction of biconditionals.
Assertion
Ref Expression
orbile ((ac) ∪ (bc)) ≤ (((ab) →2 c) ∩ (c1 (ab)))

Proof of Theorem orbile
StepHypRef Expression
1 orbi 842 . 2 ((ac) ∪ (bc)) = (((a2 c) ∪ (b2 c)) ∩ ((c1 a) ∪ (c1 b)))
2 i2or 344 . . 3 ((a2 c) ∪ (b2 c)) ≤ ((ab) →2 c)
3 i1or 345 . . 3 ((c1 a) ∪ (c1 b)) ≤ (c1 (ab))
42, 3le2an 169 . 2 (((a2 c) ∪ (b2 c)) ∩ ((c1 a) ∪ (c1 b))) ≤ (((ab) →2 c) ∩ (c1 (ab)))
51, 4bltr 138 1 ((ac) ∪ (bc)) ≤ (((ab) →2 c) ∩ (c1 (ab)))
 Colors of variables: term Syntax hints:   ≤ wle 2   ≡ tb 5   ∪ wo 6   ∩ wa 7   →1 wi1 12   →2 wi2 13 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-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  mlaconj4  844  mlaconj  845  mlaconjolem  885
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