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Theorem u2lem2 745
 Description: Lemma for unified implication study.
Assertion
Ref Expression
u2lem2 (((a2 b) →2 a) →2 a) = 1

Proof of Theorem u2lem2
StepHypRef Expression
1 df-i2 45 . 2 (((a2 b) →2 a) →2 a) = (a ∪ (((a2 b) →2 a)a ))
2 u2lem1n 740 . . . . . 6 ((a2 b) →2 a) = a
32ran 78 . . . . 5 (((a2 b) →2 a)a ) = (aa )
4 anidm 111 . . . . 5 (aa ) = a
53, 4ax-r2 36 . . . 4 (((a2 b) →2 a)a ) = a
65lor 70 . . 3 (a ∪ (((a2 b) →2 a)a )) = (aa )
7 df-t 41 . . . 4 1 = (aa )
87ax-r1 35 . . 3 (aa ) = 1
96, 8ax-r2 36 . 2 (a ∪ (((a2 b) →2 a)a )) = 1
101, 9ax-r2 36 1 (((a2 b) →2 a) →2 a) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   →2 wi2 13 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-t 41  df-f 42  df-i2 45 This theorem is referenced by: (None)
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