Theorem binr2 518

Description: Pavicic binary logic ax-r2 36 analog. (Contributed by NM, 7-Nov-1997.)

Hypotheses

Ref	Expression
binr2.1	(a →3 b) = 1
binr2.2	(b →3 c) = 1

Assertion

Ref	Expression
binr2	(a →3 c) = 1

Proof of Theorem binr2

Step	Hyp	Ref	Expression
1		binr2.1	. . . 4 (a →3 b) = 1
2	1	i3le 515	. . 3 a ≤ b
3		binr2.2	. . . 4 (b →3 c) = 1
4	3	i3le 515	. . 3 b ≤ c
5	2, 4	letr 137	. 2 a ≤ c
6	5	lei3 246	1 (a →3 c) = 1

Syntax hints:   = wb 1  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  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by:  i3ror  532  i3lor  533  i32or  534  i32an  537