Theorem i3con1 513

Description: Contrapositive.

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 499	. 2 (b⊥ ⊥ →3 a⊥ ⊥ ) = 1
3		ax-a1 29	. 2 b = b⊥ ⊥
4		ax-a1 29	. 2 a = a⊥ ⊥
5	2, 3, 4	i33tr1 511	1 (b →3 a) = 1

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

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

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