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Theorem u5lem4 760
Description: Lemma for unified implication study.
Assertion
Ref Expression
u5lem4 (a ->5 (a ->5 (b ->5 a))) = (a ->5 (b ->5 a))
Proof of Theorem u5lem4
StepHypRef Expression
1 u5lemc1 684 . . 3 a C (a ->5 (b ->5 a))
21u5lemc4 705 . 2 (a ->5 (a ->5 (b ->5 a))) = (a' v (a ->5 (b ->5 a)))
3 u5lem3 753 . . . 4 (a ->5 (b ->5 a)) = (a' v ((a ^ b) v (a ^ b')))
43lor 70 . . 3 (a' v (a ->5 (b ->5 a))) = (a' v (a' v ((a ^ b) v (a ^ b'))))
5 ax-a3 32 . . . . 5 ((a' v a') v ((a ^ b) v (a ^ b'))) = (a' v (a' v ((a ^ b) v (a ^ b'))))
65ax-r1 35 . . . 4 (a' v (a' v ((a ^ b) v (a ^ b')))) = ((a' v a') v ((a ^ b) v (a ^ b')))
7 oridm 110 . . . . . 6 (a' v a') = a'
87ax-r5 38 . . . . 5 ((a' v a') v ((a ^ b) v (a ^ b'))) = (a' v ((a ^ b) v (a ^ b')))
93ax-r1 35 . . . . 5 (a' v ((a ^ b) v (a ^ b'))) = (a ->5 (b ->5 a))
108, 9ax-r2 36 . . . 4 ((a' v a') v ((a ^ b) v (a ^ b'))) = (a ->5 (b ->5 a))
116, 10ax-r2 36 . . 3 (a' v (a' v ((a ^ b) v (a ^ b')))) = (a ->5 (b ->5 a))
124, 11ax-r2 36 . 2 (a' v (a ->5 (b ->5 a))) = (a ->5 (b ->5 a))
132, 12ax-r2 36 1 (a ->5 (a ->5 (b ->5 a))) = (a ->5 (b ->5 a))
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->5 wi5 16
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-i5 48  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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