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Theorem u3lem14mp 794
Description: Used to prove ->1 modus ponens rule in ->3 system.
Assertion
Ref Expression
u3lem14mp ((a ->3 b')' ->3 (a ->3 (a ->3 b))) = 1
Proof of Theorem u3lem14mp
StepHypRef Expression
1 lear 161 . . . 4 (((a v b'') ^ (a v b')) ^ (a' v (a ^ b''))) =< (a' v (a ^ b''))
2 lear 161 . . . . . 6 (a ^ b'') =< b''
3 ax-a1 30 . . . . . . 7 b = b''
43ax-r1 35 . . . . . 6 b'' = b
52, 4lbtr 139 . . . . 5 (a ^ b'') =< b
65lelor 166 . . . 4 (a' v (a ^ b'')) =< (a' v b)
71, 6letr 137 . . 3 (((a v b'') ^ (a v b')) ^ (a' v (a ^ b''))) =< (a' v b)
8 ud3lem0c 279 . . 3 (a ->3 b')' = (((a v b'') ^ (a v b')) ^ (a' v (a ^ b'')))
9 u3lem5 763 . . 3 (a ->3 (a ->3 b)) = (a' v b)
107, 8, 9le3tr1 140 . 2 (a ->3 b')' =< (a ->3 (a ->3 b))
1110u3lemle1 712 1 ((a ->3 b')' ->3 (a ->3 (a ->3 b))) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->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-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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