Theorem i3con1 531

Description: Contrapositive. (Contributed by NM, 7-Nov-1997.)

Hypothesis

Ref	Expression
i3con1.1	(a⊥ →3 b⊥ ) = 1

Assertion

Ref	Expression
i3con1	(b →3 a) = 1

Proof of Theorem i3con1

Step	Hyp	Ref	Expression
1		i3con1.1	. . 3 (a⊥ →3 b⊥ ) = 1
2	1	binr1 517	. 2 (b⊥ ⊥ →3 a⊥ ⊥ ) = 1
3		ax-a1 30	. 2 b = b⊥ ⊥
4		ax-a1 30	. 2 a = a⊥ ⊥
5	2, 3, 4	i33tr1 529	1 (b →3 a) = 1

Syntax hints:   = wb 1  ^⊥ wn 4  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: (None)