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Theorem i1i2 266
Description: Correspondence between Sasaki and Dishkant conditionals.
Assertion
Ref Expression
i1i2 (a ->1 b) = (b' ->2 a')
Proof of Theorem i1i2
StepHypRef Expression
1 ax-a1 30 . . . . 5 a = a''
2 ax-a1 30 . . . . 5 b = b''
31, 22an 79 . . . 4 (a ^ b) = (a'' ^ b'')
4 ancom 74 . . . 4 (a'' ^ b'') = (b'' ^ a'')
53, 4ax-r2 36 . . 3 (a ^ b) = (b'' ^ a'')
65lor 70 . 2 (a' v (a ^ b)) = (a' v (b'' ^ a''))
7 df-i1 44 . 2 (a ->1 b) = (a' v (a ^ b))
8 df-i2 45 . 2 (b' ->2 a') = (a' v (b'' ^ a''))
96, 7, 83tr1 63 1 (a ->1 b) = (b' ->2 a')
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i1 44  df-i2 45
This theorem is referenced by:  i2i1  267  i1i2con1  268  i1i2con2  269  nom41  326  1oai1  821  2oath1i1  827  oal1  1000
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