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Theorem u3lem14aa2 793
 Description: Used to prove →1 "add antecedent" rule in →3 system. (Contributed by NM, 19-Jan-1998.)
Assertion
Ref Expression
u3lem14aa2 (a3 (a3 (b3 (b3 a ) ))) = 1

Proof of Theorem u3lem14aa2
StepHypRef Expression
1 u3lem13a 789 . . . . 5 (b3 (b3 a ) ) = (b1 a)
2 u3lem13b 790 . . . . . 6 ((b3 a ) →3 b ) = (b1 a)
32ax-r1 35 . . . . 5 (b1 a) = ((b3 a ) →3 b )
41, 3ax-r2 36 . . . 4 (b3 (b3 a ) ) = ((b3 a ) →3 b )
54ud3lem0a 260 . . 3 (a3 (b3 (b3 a ) )) = (a3 ((b3 a ) →3 b ))
65ud3lem0a 260 . 2 (a3 (a3 (b3 (b3 a ) ))) = (a3 (a3 ((b3 a ) →3 b )))
7 u3lem14aa 792 . 2 (a3 (a3 ((b3 a ) →3 b ))) = 1
86, 7ax-r2 36 1 (a3 (a3 (b3 (b3 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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