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Theorem u3lem14aa2 793
Description: Used to prove ->1 "add antecedent" rule in ->3 system.
Assertion
Ref Expression
u3lem14aa2 (a ->3 (a ->3 (b ->3 (b ->3 a')'))) = 1
Proof of Theorem u3lem14aa2
StepHypRef Expression
1 u3lem13a 789 . . . . 5 (b ->3 (b ->3 a')') = (b ->1 a)
2 u3lem13b 790 . . . . . 6 ((b ->3 a') ->3 b') = (b ->1 a)
32ax-r1 35 . . . . 5 (b ->1 a) = ((b ->3 a') ->3 b')
41, 3ax-r2 36 . . . 4 (b ->3 (b ->3 a')') = ((b ->3 a') ->3 b')
54ud3lem0a 260 . . 3 (a ->3 (b ->3 (b ->3 a')')) = (a ->3 ((b ->3 a') ->3 b'))
65ud3lem0a 260 . 2 (a ->3 (a ->3 (b ->3 (b ->3 a')'))) = (a ->3 (a ->3 ((b ->3 a') ->3 b')))
7 u3lem14aa 792 . 2 (a ->3 (a ->3 ((b ->3 a') ->3 b'))) = 1
86, 7ax-r2 36 1 (a ->3 (a ->3 (b ->3 (b ->3 a')'))) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4  1wt 8   ->1 wi1 12   ->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-i1 44  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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