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Theorem 0i1 273
Description: Antecedent of 0 on Sasaki conditional.
Assertion
Ref Expression
0i1 (0 ->1 a) = 1
Proof of Theorem 0i1
StepHypRef Expression
1 df-i1 44 . 2 (0 ->1 a) = (0' v (0 ^ a))
2 ax-a2 31 . . 3 (0' v (0 ^ a)) = ((0 ^ a) v 0')
3 df-f 42 . . . . 5 0 = 1'
43con2 67 . . . 4 0' = 1
54lor 70 . . 3 ((0 ^ a) v 0') = ((0 ^ a) v 1)
62, 5ax-r2 36 . 2 (0' v (0 ^ a)) = ((0 ^ a) v 1)
7 or1 104 . 2 ((0 ^ a) v 1) = 1
81, 6, 73tr 65 1 (0 ->1 a) = 1
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-a4 33  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-t 41  df-f 42  df-i1 44
This theorem is referenced by:  oa3-2lema  978  oa3-2to2s  990
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