Theorem u3lemnob 654

Description: Lemma for Kalmbach implication study.

Assertion

Ref	Expression
u3lemnob	((a ->3 b)_|_ v b) = (a v b)

Proof of Theorem u3lemnob

Step	Hyp	Ref	Expression
1		u3lemanb 599	. . 3 ((a ->3 b) ^ b_|_) = (a_|_ ^ b_|_)
2		anor1 80	. . 3 ((a ->3 b) ^ b_|_) = ((a ->3 b)_|_ v b)_|_
3		anor3 82	. . 3 (a_|_ ^ b_|_) = (a v b)_|_
4	1, 2, 3	3tr2 61	. 2 ((a ->3 b)_|_ v b)_|_ = (a v b)_|_
5	4	con1 63	1 ((a ->3 b)_|_ v b) = (a v 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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