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Theorem i5lei2 348
 Description: Relevance implication is l.e. Dishkant implication.
Assertion
Ref Expression
i5lei2 (a5 b) ≤ (a2 b)

Proof of Theorem i5lei2
StepHypRef Expression
1 lear 161 . . . 4 (ab) ≤ b
2 lear 161 . . . 4 (ab) ≤ b
31, 2lel2or 170 . . 3 ((ab) ∪ (ab)) ≤ b
43leror 152 . 2 (((ab) ∪ (ab)) ∪ (ab )) ≤ (b ∪ (ab ))
5 df-i5 48 . 2 (a5 b) = (((ab) ∪ (ab)) ∪ (ab ))
6 df-i2 45 . 2 (a2 b) = (b ∪ (ab ))
74, 5, 6le3tr1 140 1 (a5 b) ≤ (a2 b)
 Colors of variables: term Syntax hints:   ≤ wle 2  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →2 wi2 13   →5 wi5 16 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-i2 45  df-i5 48  df-le1 130  df-le2 131 This theorem is referenced by:  oago3.21x  890  wdwom  1104
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