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Theorem i1id 275
Description: Identity law for Sasaki conditional.
Assertion
Ref Expression
i1id (a ->1 a) = 1
Proof of Theorem i1id
StepHypRef Expression
1 df-i1 44 . 2 (a ->1 a) = (a' v (a ^ a))
2 ax-a2 31 . . 3 (a' v a) = (a v a')
3 anidm 111 . . . 4 (a ^ a) = a
43lor 70 . . 3 (a' v (a ^ a)) = (a' v a)
5 df-t 41 . . 3 1 = (a v a')
62, 4, 53tr1 63 . 2 (a' v (a ^ a)) = 1
71, 6ax-r2 36 1 (a ->1 a) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->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:  oa3-2lemb  979
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