Theorem bina4 285

Description: Pavicic binary logic ax-a4 analog. (Contributed by NM, 5-Nov-1997.)

Assertion

Ref	Expression
bina4	(b →3 (a ∪ b)) = 1

Proof of Theorem bina4

Step	Hyp	Ref	Expression
1		leo 158	. . 3 b ≤ (b ∪ a)
2		ax-a2 31	. . 3 (b ∪ a) = (a ∪ b)
3	1, 2	lbtr 139	. 2 b ≤ (a ∪ b)
4	3	lei3 246	1 (b →3 (a ∪ b)) = 1

Syntax hints:   = wb 1   ∪ 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:  i3ror  532  i3th2  544