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Theorem 1i1 274
Description: Antecedent of 1 on Sasaki conditional.
Assertion
Ref Expression
1i1 (1 ->1 a) = a
Proof of Theorem 1i1
StepHypRef Expression
1 df-i1 44 . 2 (1 ->1 a) = (1' v (1 ^ a))
2 df-f 42 . . . . 5 0 = 1'
32ax-r1 35 . . . 4 1' = 0
4 ancom 74 . . . . 5 (1 ^ a) = (a ^ 1)
5 an1 106 . . . . 5 (a ^ 1) = a
64, 5ax-r2 36 . . . 4 (1 ^ a) = a
73, 62or 72 . . 3 (1' v (1 ^ a)) = (0 v a)
8 ax-a2 31 . . . 4 (0 v a) = (a v 0)
9 or0 102 . . . 4 (a v 0) = a
108, 9ax-r2 36 . . 3 (0 v a) = a
117, 10ax-r2 36 . 2 (1' v (1 ^ a)) = a
121, 11ax-r2 36 1 (1 ->1 a) = a
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8  0wf 9   ->1 wi1 12
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44
This theorem is referenced by:  oa3-6lem  980
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