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Theorem i5lei4 350
Description: Relevance implication is l.e. non-tollens implication.
Assertion
Ref Expression
i5lei4 (a ->5 b) =< (a ->4 b)
Proof of Theorem i5lei4
StepHypRef Expression
1 leo 158 . . . 4 a' =< (a' v b)
21leran 153 . . 3 (a' ^ b') =< ((a' v b) ^ b')
32lelor 166 . 2 (((a ^ b) v (a' ^ b)) v (a' ^ b')) =< (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b'))
4 df-i5 48 . 2 (a ->5 b) = (((a ^ b) v (a' ^ b)) v (a' ^ b'))
5 df-i4 47 . 2 (a ->4 b) = (((a ^ b) v (a' ^ b)) v ((a' v b) ^ b'))
63, 4, 5le3tr1 140 1 (a ->5 b) =< (a ->4 b)
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4   v wo 6   ^ wa 7   ->4 wi4 15   ->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-i4 47  df-i5 48  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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