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Theorem i4i3 271
Description: Correspondence between Kalmbach and non-tollens conditionals.
Assertion
Ref Expression
i4i3 (a ->4 b) = (b' ->3 a')
Proof of Theorem i4i3
StepHypRef Expression
1 ax-a1 30 . . . 4 b = b''
21ud4lem0a 262 . . 3 (a ->4 b) = (a ->4 b'')
3 ax-a1 30 . . . 4 a = a''
43ud4lem0b 263 . . 3 (a ->4 b'') = (a'' ->4 b'')
52, 4ax-r2 36 . 2 (a ->4 b) = (a'' ->4 b'')
6 i3i4 270 . . 3 (b' ->3 a') = (a'' ->4 b'')
76ax-r1 35 . 2 (a'' ->4 b'') = (b' ->3 a')
85, 7ax-r2 36 1 (a ->4 b) = (b' ->3 a')
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   ->3 wi3 14   ->4 wi4 15
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-i3 46  df-i4 47
This theorem is referenced by:  nom44  329  dfi4b  500
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