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Theorem i1i2 266
 Description: Correspondence between Sasaki and Dishkant conditionals.
Assertion
Ref Expression
i1i2 (a1 b) = (b2 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 (ab) = (a b )
4 ancom 74 . . . 4 (a b ) = (b a )
53, 4ax-r2 36 . . 3 (ab) = (b a )
65lor 70 . 2 (a ∪ (ab)) = (a ∪ (b a ))
7 df-i1 44 . 2 (a1 b) = (a ∪ (ab))
8 df-i2 45 . 2 (b2 a ) = (a ∪ (b a ))
96, 7, 83tr1 63 1 (a1 b) = (b2 a )
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ 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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