Theorem u1lem5 743

Description: Lemma for unified implication study.

Assertion

Ref	Expression
u1lem5	(a ->1 (a ->1 b)) = (a ->1 b)

Proof of Theorem u1lem5

Step	Hyp	Ref	Expression
1		df-i1 43	. 2 (a ->1 (a ->1 b)) = (a_|_ v (a ^ (a ->1 b)))
2		ancom 68	. . . . 5 (a ^ (a ->1 b)) = ((a ->1 b) ^ a)
3		u1lemaa 582	. . . . 5 ((a ->1 b) ^ a) = (a ^ b)
4	2, 3	ax-r2 35	. . . 4 (a ^ (a ->1 b)) = (a ^ b)
5	4	lor 66	. . 3 (a_|_ v (a ^ (a ->1 b))) = (a_|_ v (a ^ b))
6		df-i1 43	. . . 4 (a ->1 b) = (a_|_ v (a ^ b))
7	6	ax-r1 34	. . 3 (a_|_ v (a ^ b)) = (a ->1 b)
8	5, 7	ax-r2 35	. 2 (a_|_ v (a ^ (a ->1 b))) = (a ->1 b)
9	1, 8	ax-r2 35	1 (a ->1 (a ->1 b)) = (a ->1 b)

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->1 wi1 13

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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