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Theorem i3th4 546
Description: Theorem for Kalmbach implication.
Assertion
Ref Expression
i3th4 (a ->3 (b ->3 b)) = 1
Proof of Theorem i3th4
StepHypRef Expression
1 i31 520 . 2 (a ->3 1) = 1
2 i3id 251 . . . . 5 (b ->3 b) = 1
32ax-r1 35 . . . 4 1 = (b ->3 b)
43li3 252 . . 3 (a ->3 1) = (a ->3 (b ->3 b))
54rbi 98 . 2 ((a ->3 1) == 1) = ((a ->3 (b ->3 b)) == 1)
61, 5wed 441 1 (a ->3 (b ->3 b)) = 1
Colors of variables: term
Syntax hints:   = wb 1  1wt 8   ->3 wi3 14
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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