Theorem u3lem12 770

Description: Lemma for unified implication study.

Assertion

Ref	Expression
u3lem12	(a ->3 (a ->3 b_|_))_|_ = (a ^ b)

Proof of Theorem u3lem12

Step	Hyp	Ref	Expression
1		lem4 493	. . 3 (a ->3 (a ->3 b_|_)) = (a_|_ v b_|_)
2	1	ax-r4 36	. 2 (a ->3 (a ->3 b_|_))_|_ = (a_|_ v b_|_)_|_
3		df-a 39	. . 3 (a ^ b) = (a_|_ v b_|_)_|_
4	3	ax-r1 34	. 2 (a_|_ v b_|_)_|_ = (a ^ b)
5	2, 4	ax-r2 35	1 (a ->3 (a ->3 b_|_))_|_ = (a ^ b)

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->3 wi3 15

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-i3 45  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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