Theorem bina1 274

Description: Pavicic binary logic ax-a1 analog.

Assertion

Ref	Expression
bina1	(a ->3 a_|__|_) = 1

Proof of Theorem bina1

Step	Hyp	Ref	Expression
1		i3id 243	. 2 (a ->3 a) = 1
2		ax-a1 29	. . . 4 a = a_|__|_
3	2	li3 244	. . 3 (a ->3 a) = (a ->3 a_|__|_)
4	3	bi1 110	. 2 ((a ->3 a) == (a ->3 a_|__|_)) = 1
5	1, 4	wwbmp 197	1 (a ->3 a_|__|_) = 1

Syntax hints:   = wb 1  _|_wn 4  1wt 9   ->3 wi3 15

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

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i3 45

metamath.org