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Theorem i2i1 267
Description: Correspondence between Sasaki and Dishkant conditionals.
Assertion
Ref Expression
i2i1 (a ->2 b) = (b' ->1 a')
Proof of Theorem i2i1
StepHypRef Expression
1 ax-a1 30 . . 3 a = a''
21ud2lem0b 259 . 2 (a ->2 b'') = (a'' ->2 b'')
3 ax-a1 30 . . 3 b = b''
43ud2lem0a 258 . 2 (a ->2 b) = (a ->2 b'')
5 i1i2 266 . 2 (b' ->1 a') = (a'' ->2 b'')
62, 4, 53tr1 63 1 (a ->2 b) = (b' ->1 a')
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   ->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:  nom40  325  nom41  326  nom42  327  nom43  328  nom44  329  nom45  330  nom50  331  nom51  332  nom52  333  nom53  334  nom54  335  nom55  336  oal2  999
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