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Theorem lem3.3.3lem1 1049
 Description: Lemma for lem3.3.3 1052.
Assertion
Ref Expression
lem3.3.3lem1 (a5 b) ≤ (a1 b)

Proof of Theorem lem3.3.3lem1
StepHypRef Expression
1 ax-a2 31 . . 3 ((ab) ∪ (ab )) = ((ab ) ∪ (ab))
2 lea 160 . . . 4 (ab ) ≤ a
32leror 152 . . 3 ((ab ) ∪ (ab)) ≤ (a ∪ (ab))
41, 3bltr 138 . 2 ((ab) ∪ (ab )) ≤ (a ∪ (ab))
5 df-id5 1047 . 2 (a5 b) = ((ab) ∪ (ab ))
6 df-i1 44 . 2 (a1 b) = (a ∪ (ab))
74, 5, 6le3tr1 140 1 (a5 b) ≤ (a1 b)
 Colors of variables: term Syntax hints:   ≤ wle 2  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →1 wi1 12   ≡5 wid5 22 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 This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44  df-le1 130  df-le2 131  df-id5 1047 This theorem is referenced by:  lem3.3.3lem3  1051
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