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Theorem i3orlem1 552
 Description: Lemma for Kalmbach implication OR builder.
Assertion
Ref Expression
i3orlem1 ((ac) ∩ ((ac) ∪ (bc))) ≤ ((ac) →3 (bc))

Proof of Theorem i3orlem1
StepHypRef Expression
1 leor 159 . 2 ((ac) ∩ ((ac) ∪ (bc))) ≤ ((((ac) ∩ (bc)) ∪ ((ac) ∩ (bc) )) ∪ ((ac) ∩ ((ac) ∪ (bc))))
2 df-i3 46 . . 3 ((ac) →3 (bc)) = ((((ac) ∩ (bc)) ∪ ((ac) ∩ (bc) )) ∪ ((ac) ∩ ((ac) ∪ (bc))))
32ax-r1 35 . 2 ((((ac) ∩ (bc)) ∪ ((ac) ∩ (bc) )) ∪ ((ac) ∩ ((ac) ∪ (bc)))) = ((ac) →3 (bc))
41, 3lbtr 139 1 ((ac) ∩ ((ac) ∪ (bc))) ≤ ((ac) →3 (bc))
 Colors of variables: term Syntax hints:   ≤ wle 2  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →3 wi3 14 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-i3 46  df-le1 130  df-le2 131 This theorem is referenced by:  i3orlem2  553  i3orlem3  554
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