Theorem wcon3 201

Description: Weak contraposition.

Hypothesis

Ref	Expression
wcon3.1	(a⊥ ≡ b) = 1

Assertion

Ref	Expression
wcon3	(a ≡ b⊥ ) = 1

Proof of Theorem wcon3

Step	Hyp	Ref	Expression
1		ax-a1 29	. . . . 5 b = b⊥ ⊥
2	1	ax-r1 34	. . . 4 b⊥ ⊥ = b
3	2	lbi 89	. . 3 (a⊥ ≡ b⊥ ⊥ ) = (a⊥ ≡ b)
4		wcon3.1	. . 3 (a⊥ ≡ b) = 1
5	3, 4	ax-r2 35	. 2 (a⊥ ≡ b⊥ ⊥ ) = 1
6	5	wcon1 199	1 (a ≡ b⊥ ) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5  1wt 9

This theorem is referenced by:  wlecon 377  wcomd 400  wfh1 405

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-b 38  df-a 39

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