Theorem bina5 286

Description: Pavicic binary logic ax-a5 analog. (Contributed by NM, 5-Nov-1997.)

Assertion

Ref	Expression
bina5	(b →3 (a ∪ a⊥ )) = 1

Proof of Theorem bina5

Step	Hyp	Ref	Expression
1		le1 146	. . 3 b ≤ 1
2		df-t 41	. . 3 1 = (a ∪ a⊥ )
3	1, 2	lbtr 139	. 2 b ≤ (a ∪ a⊥ )
4	3	lei3 246	1 (b →3 (a ∪ a⊥ )) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6  1wt 8   →₃ wi3 14

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131

This theorem is referenced by: (None)