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Theorem lei2 346
Description: "Less than" analogue is equal to ->2 implication.
Assertion
Ref Expression
lei2 (a =<2 b) = (a ->2 b)
Proof of Theorem lei2
StepHypRef Expression
1 mi 125 . 2 ((a v b) == b) = (b v (a' ^ b'))
2 df-le 129 . 2 (a =<2 b) = ((a v b) == b)
3 df-i2 45 . 2 (a ->2 b) = (b v (a' ^ b'))
41, 2, 33tr1 63 1 (a =<2 b) = (a ->2 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6   ^ wa 7   =<2 wle2 10   ->2 wi2 13
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-b 39  df-a 40  df-t 41  df-f 42  df-i2 45  df-le 129
This theorem is referenced by: (None)
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