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Theorem u1lemob 630
Description: Lemma for Sasaki implication study.
Assertion
Ref Expression
u1lemob ((a ->1 b) v b) = (a' v b)
Proof of Theorem u1lemob
StepHypRef Expression
1 df-i1 44 . . 3 (a ->1 b) = (a' v (a ^ b))
21ax-r5 38 . 2 ((a ->1 b) v b) = ((a' v (a ^ b)) v b)
3 or32 82 . . 3 ((a' v (a ^ b)) v b) = ((a' v b) v (a ^ b))
4 ax-a2 31 . . . 4 ((a' v b) v (a ^ b)) = ((a ^ b) v (a' v b))
5 lear 161 . . . . . 6 (a ^ b) =< b
6 leor 159 . . . . . 6 b =< (a' v b)
75, 6letr 137 . . . . 5 (a ^ b) =< (a' v b)
87df-le2 131 . . . 4 ((a ^ b) v (a' v b)) = (a' v b)
94, 8ax-r2 36 . . 3 ((a' v b) v (a ^ b)) = (a' v b)
103, 9ax-r2 36 . 2 ((a' v (a ^ b)) v b) = (a' v b)
112, 10ax-r2 36 1 ((a ->1 b) v b) = (a' v b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i1 44  df-le1 130  df-le2 131
This theorem is referenced by:  u1lemnanb  655  u12lem  771  salem1  837
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