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Theorem i2id 276
Description: Identity law for Dishkant conditional.
Assertion
Ref Expression
i2id (a ->2 a) = 1
Proof of Theorem i2id
StepHypRef Expression
1 df-i2 45 . 2 (a ->2 a) = (a v (a' ^ a'))
2 anidm 111 . . . 4 (a' ^ a') = a'
32lor 70 . . 3 (a v (a' ^ a')) = (a v a')
4 df-t 41 . . . 4 1 = (a v a')
54ax-r1 35 . . 3 (a v a') = 1
63, 5ax-r2 36 . 2 (a v (a' ^ a')) = 1
71, 6ax-r2 36 1 (a ->2 a) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  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
This theorem is referenced by:  oago3.29  889
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