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Theorem i5lei2 348
Description: Relevance implication is less than or equal to Dishkant implication. (Contributed by NM, 26-Jun-2003.)
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  1106
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