Theorem binr1 499

Description: Pavicic binary logic ax-r1 analog.

Hypothesis

Ref	Expression
binr1.1	(a →3 b) = 1

Assertion

Ref	Expression
binr1	(b⊥ →3 a⊥ ) = 1

Proof of Theorem binr1

Step	Hyp	Ref	Expression
1		binr1.1	. . . 4 (a →3 b) = 1
2	1	i3le 497	. . 3 a ≤ b
3	2	lecon 146	. 2 b⊥ ≤ a⊥
4	3	lei3 238	1 (b⊥ →3 a⊥ ) = 1

Syntax hints:   = wb 1  ^⊥ wn 4  1wt 9   →₃ wi3 15

This theorem is referenced by:  i3con1 513  i3ran 517  i3i0tr 524

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

metamath.org