Theorem u2lemnona 648

Description: Lemma for Dishkant implication study.

Assertion

Ref	Expression
u2lemnona	((a ->2 b)_|_ v a_|_) = (a_|_ v b_|_)

Proof of Theorem u2lemnona

Step	Hyp	Ref	Expression
1		u2lemaa 583	. . 3 ((a ->2 b) ^ a) = (a ^ b)
2		df-a 39	. . 3 ((a ->2 b) ^ a) = ((a ->2 b)_|_ v a_|_)_|_
3		df-a 39	. . 3 (a ^ b) = (a_|_ v b_|_)_|_
4	1, 2, 3	3tr2 61	. 2 ((a ->2 b)_|_ v a_|_)_|_ = (a_|_ v b_|_)_|_
5	4	con1 63	1 ((a ->2 b)_|_ v a_|_) = (a_|_ v b_|_)

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->2 wi2 14

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-i2 44  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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