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Theorem i5lei2 348
Description: Relevance implication is l.e. Dishkant implication.
Assertion
Ref Expression
i5lei2 (a ->5 b) =< (a ->2 b)
Proof of Theorem i5lei2
StepHypRef Expression
1 lear 161 . . . 4 (a ^ b) =< b
2 lear 161 . . . 4 (a' ^ b) =< b
31, 2lel2or 170 . . 3 ((a ^ b) v (a' ^ b)) =< b
43leror 152 . 2 (((a ^ b) v (a' ^ b)) v (a' ^ b')) =< (b v (a' ^ b'))
5 df-i5 48 . 2 (a ->5 b) = (((a ^ b) v (a' ^ b)) v (a' ^ b'))
6 df-i2 45 . 2 (a ->2 b) = (b v (a' ^ b'))
74, 5, 6le3tr1 140 1 (a ->5 b) =< (a ->2 b)
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4   v 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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